Here are the links to the state government pet laws in Australia. If you are planning to move interstate with your cat or dog, review the state government pet laws in Australia.
Australian Capital Territory
ACT Government, Domestic Animals
New South Wales
NSW Division of Local Government, Cats and Dogs
Northern Territory
Alice Springs Town Council, Pets
Queensland
QLD Government, Pets and Animals
South Australia
South Australia, Dog and Cat Board
Tasmania
TAS Local Government Division, Dogs
Victoria
Department of Environment and Primary Industries, Pets
Western Australia
WA Department of Local Government, responsible cat ownership
WA Department of Local Government, how to be a responsible dog owner