I will try to answer nanoboy and tetropod together. This answer is based on the situation in Victoria, the situation in other states will vary. Also because I am not involved much with private breeders, my understanding of their situation may be a little out.
Firstly to the question of collections open to the public. There are two licences, a wildlife park licence and a zoo licence. Wildlife park licences are restricted to native animals, while zoo licences can also keep exotics. Basicly there is no difference beween the two, I imagine zoo licence holders are subject to greater scrutiny because of the threat of escape of dangerous and pest species. There are basic husbandry requirements plus minimum cage size. However as long as these are met public collections can keep any animal they can legally obtain.
Private collections are largely restricted to native animals. The different species are classified according the their conservation status and availability from private sources. There are four levels - no licence needed, level 1 and leve 2 licences and lastly not on the schedule, so cannot be held. As far as mammals go, the on licence species include some kangaroos and wallabies, sugar gliders, some possums, dingoes, but not wombats and quolls.
There is no licence required for exotics however the only exotics that can be kept are fish, a number of bird species and 6 species of deer, blackbuck, American bison, water buffalo, and camels. Some people keep some other exotics under "sunset" clauses, ie monkeys, on the condition that they cannot transfer to another private owner or breed their animals.
Hope that helps