Best advice is not to rush choosing OB and hospital...do it once you arrive here (not before), take your time, take the hospital tours, THEN decide. Good idea is to have an OB as soon as you arrive, but you don't have to commit to that OB for the birth. As someone suggested, that OB can be as a back up in case you need help.
Be warned -- all OB's here want you sign up and commit to them (pay deposits up front) soon after you start seeing them - they are all in private practice, none are public. Hospitals are the same. I got sucked into doing this and now regret it - once I paid the deposits the service dropped of dramatically --- lengthy waits each month for an appt, rushed 2-minute OB check-ups where they forgot to do things like take my blood pressure etc. So...don't get pushed into signing up until you've seen all the OB's you want, taken all the hospital tours and are completely satisfied with your choice. Once you start making friends here with other expat mums you will begin hearing stories and getting some great advice....it's worth it to wait until you're settled before you make a final choice.
As for your questions:
1. GPs and OBs cost the same - better off with an OB. You don't want a local GP for OB stuff, and western GPs are good, but very very busy. It's not mandatory to have an OB but makes better sense here. There are no birthing centres that I know of. The hospital and OB you choose will be an important factor in getting the birth you want - hospital more than OB I feel, as nurses do the majority of the birth experience anyway. There is one OB here -- Dr Ann Hagarty -- at Mt Elizabeth who I am told is excellent with vaginal deliveries with little intervention.
2. No referral needed to see an OB. Just call and turn up. Bring your Australian medical file if you like from your Australian GP/OB - they do like that. I brought mine from the US and they were very grateful. Solves alot of unknowns. A copy of your medical file is a right, so just ask your Australian doctor.
3. An OB is not a requirement to book a hospital, but you do have to have an OB who is registered with the hospital to do the delivery so you will be repeatedly asked this question by the hospital. My advice is not to book the hospital until you have the OB - most doctors will only deliver in one hospital, so you don't want to lock into a hospital if you then find the OB of your dreams only delivers in another hospital. For hospitals, you call, ask when they do maternity tours, turn up and that's it. Some will do the hard sell -- don't fall for it. Take your time. Tours cost nothing. Where you live has no bearing on which hospital you can choose - Singapore is a small place, so any hospital will be within easy distance anyway. You can choose any hospital you like.
4. From own research (am having second in January 06 and also arrived here at 11 weeks pregnant) TMC is a good hospital for an uncomplicated vaginal delivery. Mine is an elective c-section, therefore, I'm looking elsewhere. I think, from what other mums say here, a birthing centre experience in Singapore is dependent upon the OB you choose.
5. The only reason I would go back to Australia to do the birth is if you are dead set on having the birthing centre experience again and you can't find it here. It's an expensive, time consuming option for you, but I can totally understand that if you put a lot of effort and research into your first birth and you just want the same thing again that you mind find it easier to just go back to Australian and do it there. God knows in the past week I have longed myself to just go back to America and do my second birth there. At least in America I know what to expect, what I want, where to do etc, and I can guaranteed the same experience. It's a personal choice -- so that's why I say TAKE YOUR TIME HERE to find the right OB and hospital.
6. You cannot do a scan here without being under the care of an OB or GP. A GP will probably refer you to an OB who will then schedule the scan. So much easier to get an OB when you arrive and get the scan done. You settle the account when you leave, without having to commit to the hospital or the OB. Ultrasound centres are in all the hospitals -- don't know of any that are separate from a hospital.
Good luck!