I think, however, you should be aware that getting around with a toddler is a lot more difficult than in other places. Firstly running a car is very expensive. You're looking at SGD2000 pcm all in for leasing, petrol and tolls, and that's for a "normal" family car. Taxis are easily available and cheap and many people use them and do without a car, but they are not toddler-friendly. There are no child seats provided, and often not even any rear seat belts. You'll have to sit with the child on your knee unless you want to carry a baby seat around with you (not recommended in the heat).
Although there are lots of buses and an excellent MRT system, using them with a child in a push chair can be very difficult and almost impossible at peak hours.
There are things to do with kids such as playgrounds, swimming pools, etc but the daytime heat can make many outdoor activities something of an ordeal. There's cable TV with the Disney Channel however, so don't despair.
Hope this is not too negative. I'm sure you'll find Singapore an interesting experience, but I think its wisest to be prepared for what you'll find.