I was like your daughter - a growing chest at aged 9 and full-on puberty with all the trimmings (hormonal and otherwise) done and dusted by age 11.
My mum didn't cope well and i found out everything she should have told me from a friend who had a very hippy type mum (she explained the birds and bees to her daughter with some extracts from The Joy of Sex for goodness sake!!). My mum's response was to buy me a couple of books (one about periods the other, a beautifully illustrated book about pregnancy mainly). They were given to me in a carrier bag and never spoken of again.
When the time came for periods I told her and was given a warehouse sized box of sanitary towels so I didn't have to ask again for any for about 2 years and when I started having sex with my boyfriend many years later, it was my grandmother who came with me to the clinic to get the pill.
The moral of the story I guess being that I never felt comfortable talking about any of these things to my mother and I trace it back to how she dealt with my puberty at such a young age.
Yes its tough to talk about adult things with a young child, but her body is changing and right now she needs more than anything to know that she can ask her mum anything (and i mean anything because unlike the 13 years olds going through this together, she is all alone - none of her friends are going through this and you can bet she isn't asking them if this or that is normal!)
Taking the lead and starting the conversation is tough but bite the bullet , its just a new stage of parenting. The little girl isn't lost forever, but the bigger girl soon to come is making her slow debut and needs help. I have a sister 18 years younger than me and I was the one she put all her questions too at about 9 years old.
I concentrated on talking to her about how all girls go through this, but at different times. That whatever she thinks, what is happening to her body is normal and nothing to be scared of. As for the birds and the bees, well be prepared - buy some books but obviously read them first and use them as a tool to aid your talks to her.
Just enter "where do babies come from" into the Amazon.com website and you'll find a whole selection of books, esp stuff aimed at the late primary age. They do deliver worldwide if you find a book you can't get in singapore yourself.
Be proud of yourself for looking for help in approaching this sensitive subject with your daughter - I'm sure it will all work out just fine. x