Hmmm....not sure that Singapore has joined up with Australia and New Zealand yet, but never mind.
Our two were 12 and 7 when we went in 2006. We were in Singapore for a week and then joined the Pacific Sky for seven nights. The kids loved it and so did we.
The zoo has a well deserved reputation for excellence, that needs to be a must-do (the night zoo was OK but got rained out just as the main show started). There is also a massive bird park that was simply awesome.
Sentosa Island is well worth a visit for a day. It keeps changing the attractions so perhaps check that out on the web. In the eveing they have a light show. We went and thought it was magnificent....but get there early, it gets packed.
Another thing that we did that we all enjoyed was a day tour to a fish farm in Malaysia. It was worth it just to see the border crossing! But it also visited a rubber plantation, an orchid farm and the fish farm was fun.
Singapore is reglarly updating everything so check it out on the web first. It rains every afternoon for about an hour, it will be hot and steamy, the cabs are dirt cheap and nothing is very far away (do not even consider driving yourself around, when you get there you'll see why!) It's modern, fun and I'm sure the whole family will love it.