After baby came, we didn't notice that much of a jump in our living expenses, I think because we did not go out to restaurants, movies, and bars as much!
It is possible to purchase second hand baby gear. Or if you want brand new, I found that:
New cribs cost about $300 - $500.
Prams are anywhere from $150 to $700. Carseats are about $180 and up.
Try surfing some websites of shops here to compare prices before you come.
There is a wide price range of clothes, shoes, and toys in Singapore but the selection is not as good as, say Australia or US/Canada.