Keeping native (freshwater) turtles as pets requires special care and is subject to permit or licensing restrictions. These vary between states and territories so you need to contact your state/territory government (the Department of Environment or its equivalent) to find out what restrictions apply.
The Turtles Australia website has information on permits and the care and husbandry of turtles:
As with all pets, we recommend you do plenty of research before you consider taking on a turtle. Turtles require special care and live for many years, so deciding to have one as a pet is a big commitment. You also need to ensure that you obtain your turtle from a reputable breeder and make sure that it has not been taken from the wild (this is illegal in most States).
If you find an injured turtle, contact an Australian wildlife rescue volunteer near you by visiting the Australian Fauna Care Network at: