Well, I've lived in Australia for a good number of years, so hopefully I can shed some basic insight into your question.
Work CultureFirst off, generally speaking Aussies are a fairly cruisy lot. I'm speaking in general and it obviously can differ vocation to vocation and work environment to work environment.
They will work hard when they work but not slave at work, and they play hard when they're on their off days.
They don't really like it when you work too hard - in the sense where by you stay back late everyday and have no life. They would probably see it as something unnecessary (kissing the boss's @rse, boss's pet, nerd, threat - alien culture).
In that case they would probably tell you to 'have a stubby', 'lighten up', 'have a life', 'relax' - invite you for drinks after work.
Work environment wise they are fairly casual and there isn't a funeral atmosphere like in many Asian workplaces.
Most work environments are 9 - 5pm, 5 days a week affairs, unless they specific you have to work an additional day. This should be covered for and your wage should be overtime, not normal wages.
Because they are generally quite 'casual' compared to an Asian workplace it might be considered more 'relaxed' (but it doesn't mean you can slack in quality of work!) you might find there is a fair amount of casual conversation, sometimes lots of jokes and many of these jokes can be considered 'un-PC' (Asian/Racial jokes, hangover jokes, etc) but its never usually malicious.
Most Aussie work environments do not adhere to the typical Asian hierarchy. There is no 'treat the elder as God' or 'treat the boss and your superiors like deity' culture and they actually prefer you to be assertive, outspoken and diverse in your views.
They want to hear your output, even if you're going against their views. (Of course you still have to remember basic courtesy and diplomacy)
Very unlike the 'tip toe around the boss' and 'give boss the first chair at gatherings' expected of you in Asian work places.
Because of its casualness you might find that you don't relate to their humour because of cultural and racial/national differences. It doesn't mean that they are isolating you its just that many of them do not really understand the differences, but they are always happy that you take an interest in Aussie culture and humour.
Some no-no's are obviously malicious racist jokes, 'who's country is better' unless you're invited to debate (Many Aussies seem to have some hang ups about Singapore, whether they misinformed or whatever.), discussing personal issues because of the casual atmosphere (Aussies seem to have different sets of friends which are distinctly separate so they are very casual and conversations can be very 'superficial' or shallow to a certain extent because going beyond that can make them feel uncomfortable.) and working too hard.
Soon after you'll probably lighten up and see it as a breath of fresh air compared to an uptight, hierarchical work culture in Singapore.
Friends/PeopleThere are plenty of Asians, especially SE-Asians in Australian cities such as Sydney, Perth and Melbourne.
However, I wouldn't recommend you just mix with them. Try to spread out and diversify your friendship circle.
Of course, you would probably feel a little lonely because of the lack of cultural closeness we Asians seem to have in terms of friendship which might differ in other cultural friendships, but it would isolate you even more if you just mix with them.
Shopping/ServicesThough this is slowly changing - shops and services usually close at 5pm and many close on Sundays. In Perth its much worse, you can't do squat after 5pm and the whole city is an empty ghost town on Sundays. Being Singaporean you might find it very odd and to a large extent, probably very boring since you won't have a large amount of friends when you first come over.
However, it is a good time to socialise and set friendly 'dates' to get to know your friends better or perhaps just spending some 'quality' time for yourself to just relax without too much commercial mental stimulation.
You save lots of money too.
If in other major cities, its not as bad.
Though many close at 5pm there are plenty of food outlets and cafes and some shops in the city center which are still open for business.
Shopping centres - not as numerous and more spread out, obviously - tend to close at 5pm.
In Melbourne - not sure in other cities - they have "late night shopping" where shop hours are extended till 7pm or 9pm
You might find there is a lack of diversity in the products sold in Australia, be they supermarket products or perhaps clothing. I can't say its a good thing because I like variety but you'll get used to it.
There are usually plenty of Asian grocery stores dotted all over the place and you can get your 'Asian fix' and ingredients there. Again variety might differ.
But try your hand cooking popular Aussie fare since western ingredients will be cheaper. I remember white button mushrooms in Singapore were bloody expensive many years ago but when I was in Oz I just stuffed myself with white mushrooms so much I started to actually miss shittake. LOL.
Services are slow but its not necessarily a bad thing. At least you know service people are treated as human beings, not machines and are paid decent wages.
Banks take from a day to a couple of days to activate a bank account. Your card is not usually given to you straight away, you get them in the mail, then password comes separately. This can take up to a week.
Same goes for internet and phone lines. If wherever you're living don't already have a phone line installed you'll have to wait up to a couple of weeks for it to be installed during office hours. Ditto for internet, in some instances it might take a month for internet to be 'activated'.
I remember applying for 3 internet providers at differing periods of times and one was 2 weeks, the other was a month of waiting.
However, you can survive on dial up they provide or buy yourself a prepaid internet service while waiting if its really urgent for you to be hooked up so its not an issue.
I think service here is much better. People actually smile and attend to you. But again I don't expect someone paid a pittance in Singapore to work 12 hours a day with little or no work rights to genuinely smile at me and ask me what I want when they don't get what they want either. Haha.
But seriously, the service in Oz generally is quite good, save for many Asian cafes where you still get the snobby/'can't give a sh!t attitude' but most Asian eateries serve really cheap food in comparison to other cuisines/Aussie restaurants so I wouldn't complain.
Cheap food is between $6 (dirt cheap, hard to find) - $10 (cheap - more common) and this is usually Asian dishes. You'd probably get a deli sandwich or a wrap at around that price for 'Western' food.
Generally you should expect to pay $12 - $18, of course this varies.
Restaurants generally between $13 - $30+.
I shopped for two people and including meat it was around $80 - $100 per week. I cook alot and try out different cuisines so if you don't cook much and will only be trying the odd 'other' dish or two you can expect that to be much less.
Here's a general price list but its not exhaustive and prices might have changed a little but generally its what you can expect:
http://www.latrobe.edu.au/international/living/shopping-and-foodAsian food obviously doesn't taste like 'authentic' Asian food but when in Rome...!
Try out all the different cuisines!
I remember a friend of mine visited and complained about how terrible the Chinese food was and I asked them if they were visiting Oz to try Chinese food or to sample Aussie culture?
Needless to say they got my hint and they really did enjoy themselves and the different experience.
Safety
Safety seems to be a very overrated thing here.
I lived for a couple of years and honestly I never got mugged, called a racist name (for those who say Aussies are very racist or whatever), burgled or harassed, even.
Those 'racist' beatings you saw recently in the news, really, were perpetuated by non-white Aussies who were just looking to beat up anyone, and the Asians just happened to be in the wrong area, wrong time.
Many poorer Asians also choose dangerous areas to live in because they are cheap, work long hours resulting in coming home during the dead hours of the night and really its not a good combination anywhere in the world.
When living in any country you just have to be aware and prudent.
Common sense should apply, obviously.
Don't walk in dark streets/corners, always take well-lit paths, go with a friend if its a risky place, don't live in a dangerous/dodgy area just because it is cheap, if you're walking alone its good to call up a friend or pretend to be on the phone if you're feeling unsafe or if you think someone is following you, don't get dead drunk when alone, don't carry lots of cash and flaunt your wares (bling, laptop, etc).
It really isn't as dangerous as people make it out to be.
In fact I was actually harassed and molested in Singapore before and I never experienced those in the other countries I've lived in (Malaysia being one of them).
Does that make Singapore an unsafe place? Of course not. Bad things sometimes happen, even in safe countries.
We Singaporeans have been bred to be big wieners, afraid of everything and everywhere - even going to Malaysia is like "OH SH!T that Malaysia so dangerous ONE!" well if we didn't walk around with our SG attitudes (seriously I've seen that) inviting people to just want to mug us for the sake of mugging us just because they can't stand us well tough.
Just follow the basic protocols and don't create unsafe situations for yourself.
If it doesn't feel safe - don't do it, don't go there.
General
Australia is a large country.
So you might feel its quite 'empty' and not as buzzing as a typical Asian city.
You might even feel isolated, lonely to a certain extent.
Everyone seems to have their own lives, their own niche friends circles, and further more it can be rather alien.
Culture wise Aussies can seem rather crass at times but Aussies in general have big hearts, be they bogans (equivalent of red necks) from the faraway suburbs or your city slickers.
They can be quite passionate in many things and many take it upon themselves to take up causes such as Japanese whaling (but strangely ignore the brutal bashings of baby seal pups in Canada for the fur trade but that's another topic).
Some can be quite xenophobic but its usually against Asians or "outsiders" who do not attempt to even integrate or understand the Aussie culture, choosing to speak their own languages and immerse themselves in cultural/racial enclaves separate from normal Aussies.
Many Aussies have a fairly large exposure of Asian culture, be it somewhat shallow or sometimes misinformed, but you don't have to really explain too much to them because most Aussies cities are quite multi-cultural - not in the SG way we're used to but more like a bunch of diverse races working and thrown together in one area - so you get a good degree of exposure to other cultures as well apart from white Aussie culture.
But take it in your stride. Many S'poreans actually come and straight away enjoy this feeling of independence and freedom (first thing I saw and thought was - omfg, PORN! XD) and the whole casual, very light-hearted feeling you get while in Australia which Singapore really, really lacks.
Just PM me if you have any other questions, I'll be happy to answer them or help.
