I think things might have changed. I had reason to check this out last year and this was what I uncovered...
Hemidactylus frenatus is not to be found on the 'NSW Native Animal Keepers’ Species List 2015'. It is, however, classified as a Category 2 exotic (p40 of the ‘Non-Indigenous Animals Regulation 2012 under the Non-Indigenous Animals Act 1987’).
Category 2 is defined as “Animals that pose an extreme or more serious threat to the environment, agriculture or persons, and that are restricted to being kept in licensed animal display establishments or by:
(i) a corporation that is accredited as a research establishment under section 20 of the Animal Research Act 1985, or
(ii) an individual who holds an animal research authority issued under section 25 of the Animal Research Act 1985, or
(iii) a person who holds an animal supplier’s licence issued under section 39 of the Animal Research Act 1985).”
Unfortunately, as we are all well aware, the application and enforcement of the legislation is not particularly consistent. It varies with the particular departmental officer with whom you interact, the extent of their knowledge of the legislation, how up-to-date that is, how they slept the night before, what their morning was like and the particular direction that the wind is blowing at the time!