Nothing to add on Sydney. I did happen to like Melbourne better - so there. In Brisbane, there is a tropical bird park that your kid will enjoy.
Here is a travel page I half-finished, it has some sections on Sydney, Melbourne, etc. Kind of idiosyncratic, out-of-date, and we were on a severe budget - but might give you some flavour of the places.
http://ourworld.compuserve.com/homepages/johnliu/