hi,
I am not too sure how old your LO is but the zoo tends to be more appropriate for when they are a little older - my son's first visit at 18 months was a huge non-event, he loves animals and everything but didn't seem to be taken with anything at the zoo (maybe becos the environment was too natural?!?!)! We tried him again when he was 2 years 3 months and it was better....if you want something outdoorsy, easy to get to, stroller friendly and pleasant, I'd suggest the Botanical Gardens (opposite the American Embassy, Tanglin Road area, very near Orchard Road). It is a lovely big garden with different areas and lakes (feeding the ducks and fish - generally both babies and toddlers love that) and alot of it is shaded with giant trees if it gets too sunny.....there is also a lovely cafe or 2 there for having meals and even an airconditioned food court at the entrance if you'd like some local food - plenty of lvoely grass area to have a picnic too if you feel so inclined! And if LO protests or it gets too hot, you can leave quite easily by public transport, Orchard Road is about a brisk 10 min walk away....
have fun and enjoy Singapore!