from the Wild Animal Control Act of 1977
[(5)Except as authorised by a permit or licence that is effective for the purposes of subsection (1), no person may, without a permit issued by the Director-General,—
(a)Capture or convey or keep in captivity any thar, chamois, possum, or wallaby; or
(b)Except for the purposes of farming or operating a safari park, capture or convey or keep in captivity any deer.]
in other words, yes you do need a permit to keep a possum, wallaby etc in captivity