Hi Brian,
The Sydney area doesn't have to many places like that but I do suggest you take a trip to the Sydney Wildlife World at Darling Harbour. They have all sorts of Australian creatures there and do have a daily bird show with some fantastic native birds, well worth a look, this is the web address www.sydneywildlifeworld.com.au . If you're travelling further a field let me know and I'll give you some pointers.
Gordon.

Thanks Gordon - I will be sure to visit Wildlife World.

Brian,
You could also try Featherdale Wildlife Park. They are out in the suburbs but smaller than Tooronga Zoo. If you go on a weekday when the kids are at school you can enjoy yourself without the crowds. http://www.featherdale.com.au/index.htm

Hope you enjoy your stay in OZ.

Yes Featherdale would defiantly be worth a visit, again they have all sorts of little creatures there, thanks for that Birdy.
Gordon.