Hi Elle
We are living in SG last 3 years with our now 5 year-old. (Moving to HK in August).
Depending on the age of your toddler you might also consider a trip to the beach at East Coast Park where you can hire bikes with babyseats, A ride on the SG flyer if they are brave, a pushchair walk around the Clarke Quay riverside area (lots to look at, and bars and restaurants for yourselves), Wild wild wet waterpark, or even a little trip out to Pulau Ubin Island (catch the little ferry boat from Changi Village Pier. Bikes to hire there, lots of wildlife etc.
However.....be warned. Its usually very hot outside in the daytimes which can be uncomfortable, and it is nearly guaranteed to tip down with very heavy rain and often thunder at least once a day. So dress accordingly and bring an umbrella!
What area are you going to be staying in?
Hope this helps