You're best bet in terms of getting animals would be to become a member of the ZAA. Once people in the industry respect your zoo you will be able to trade for more exotic animals with other zoos.
To start with though you would probably want to get some Australian natives that can be held privately. Things like wallabies, snakes, lizards and insects etc. are easy to come by and will probably form the basis starting out.
If you're zoo is going well in terms of natives then some of the species you may be able to get are meerkats, marmosets and other smaller animals that are quite abundant.
Well there's deer geese barramundi eels crocodiles rainbow lorikeets brim whiting possoums mud carbs flat head sulphur cockatoos zebra finches guiena pigs pigs goats snake necked turtles bluetognues children's pythons green tree frogs chickens. Also does anybody know how to get kangaroos?