Sorry for the late reply, but here it is

Without a license
Common Eastern Froglet Crinia signifera
Eastern Banjo Frog Limnodynastes dumerilii
Plains Froglet Crinia parinsignifera
Southern Brown Tree Frog Litoria ewingii
Spotted Grass Frog Limnodynastes tasmaniensis

With a license
Blue Mountains Tree Frog Litoria citropa
Brown Striped Frog Limnodynastes peronii
Common Spadefoot Toad Neobatrachus sudelli
Dainty Green Tree Frog Litoria gracilenta
Eastern Dwarf Tree Frog Litoria fallax
Giant Barred Frog Mixophyes iteratus
Giant Tree Frog Litoria infrafrenata
Great Barred Frog Mixophyes fasciolatus
Green Tree Frog Litoria caerulea
Haswell’s Frog Paracrinia haswelli
Leaf Green Tree Frog Litoria phyllochroa
Leseur’s Frog Litoria lesueuri
Peron's Tree Frog Litoria peronii
Southern Smooth Froglet Geocrinia laevis
Water-holding Frog Cyclorana platycephala
Whistling Tree Frog Litoria verreauxii
+Previously listed frogs

With an advanced License
Giant Burrowing Frog Heleioporus australiacus
Green and Golden Bell Frog Litoria aurea
Growling Grass Frog Litoria raniformis
Magnificent Tree Frog Litoria splendida
Northern Dwarf Tree Frog Litoria bicolor
Orange Thighed Tree Frog Litoria xanthomera
Red-eyed Tree Frog Litoria chloris
Roth's Tree Frog Litoria rothii
Southern Toadlet Pseudophryne semimarmorata
+Previously listed frogs