Here's a list of amphibians approved for import into Australia, though none of them can be imported for household pets:
Andrias japonicus Japanese Giant Salamander
Eligible non-commercial purpose only, excluding household pets.
High security facilities only.
Dendrobates auratus Green and Golden Poison Arrow Frog
Eligible non-commercial purpose only, excluding household pets.
High security facilities only.
Dendrobates tinctorius Dyeing Poison Dart Frog
Eligible non-commercial purpose only, excluding household pets.
High security facilities only.
Litoria infrafrenata Giant Green Tree Frog
Eligible non-commercial purpose only, excluding household pets.
High security facilities only.
Philautus romeri Romers Tree Frog
Eligible non-commercial purpose only, excluding household pets.
High security facilities only.
Pyxicephalus adspersus adspersus African Bullfrog (southern subspecies)
Eligible non-commercial purpose only, excluding household pets.
Certified males over 14 cm snout-vent length only.
High security facilities only.
Taricha granulosa Rough Skinned Newt
Eligible non-commercial purpose only, excluding household pets.
High security facilities only.
Xenopus laevis South African Clawed Frog
Eligible non-commercial purpose only, excluding household pets.
High security facilities only.
source:
List of Specimens taken to be Suitable for Live Import
Environment Protection and Biodiversity Conservation Act 1999
http://www.deh.gov.au/biodiversity/trade-use/lists/import/pubs/live-import-list.pdf