The laws concerned with owning native and introduced animals are usually quite different and also vary according to the state in which you live. In Victoria, special permits issued by the Department of Environment, Land, Water and Planning (DELWP) are required to keep most Australian wildlife.
Most native animals are protected and cannot be kept as pets. Animals that can be kept as pets include native birds such as some parrots, cockatoos, finches, quail, doves, pigeons and ducks however these must never be caught from the wild (as this is illegal). Less common native animal pets are reptiles, some tortoises, lizards, crocodiles and snakes, some frogs, and some types of fish. Special permits are necessary to keep most Australian wildlife (e.g. kangaroos, possums, wombats, koalas, kookaburras, magpies, hawks, many reptiles, frogs and fish). Usually only zoos and fauna parks are given permits to hold these animals.
The RSPCA is actively opposed to the sale and keeping of native animals (other than captive bred birds) as pets. Due to widespread ignorance of the husbandry requirements of these animals, they often suffer from neglect. The RSPCA believes that native birds bred in captivity should always be kept in an aviary with the one exception being the budgerigar, provided that it is housed in a cage of approved size (a minimum of 30cm x 30cm x 38cm for one bird). Cockatoos must not be confined by a chain to the leg.