It is illegal to keep most native wildlife without a permit from your states Parks and Wildlife department. Import and Export permits are also required when moving native wildlife between different States/Territories. Laws vary between each State or Territory.
For more information please follow the links below.

Northern Territory
http://www.nt.gov.au/nreta/wildlife/permits/pdf/permit_keep_wildlife.pdf
http://www.nt.gov.au/nreta/wildlife/permits/keep.html

Queensland
https://www.epa.qld.gov.au/ecoaccess/plants_and_animals/recreational_use_of_animals/keeping_wildlife_for_recreational_purposes.html

South Australia
http://www.environment.sa.gov.au/Plants_and_Animals/Permits_and_Licences

Victoria
http://www.dse.vic.gov.au/CA256F310024B628/0/B26F8AF7E3D97226CA257193007930EF/$File/Application+for+a+Private+Wildlife+Licence.pdf

New South Wales
http://www.environment.nsw.gov.au/wildlifelicences/GettingAReptileKeepersLicence.htm