I agree that it's definitely a legless lizard or Pygopod of the genus Delma and probably D. tincta.
You have to be very careful not to confuse these with juvenile brown snakes (Pseudonaja sp.) which are highly venomous as you no doubt know.
I can see that you're a vet science student, so I don't want to assume that you don't know how to handle herps, however I should advise that it's best not to handle an unknown species and although you're restraining its head, there's still a risk of being bitten.
Identifying features that distinguish legless lizards from snakes is the very long tail of the former, compared to the latter. The tail starts at the vent, which is clearly seen in your photo. Snakes like Pseudonaja sp. have a relatively short tail (~20% of snout-vent length), whereas Pygopods have relatively long tails that are always longer than the body (if it's the original tail i.e not regrown) in all species that I know of. I don't know D. tincta but other closely related Delma sp. tails are around 200-250% of S-V length. Look for the point where the body noticeably tapers, which approximates where the vent is.
There are some other features to look for, like a single dark nape band in brown snakes compared to two in Delma. Also look for tiny ear holes that are present in all Pygopods but not in snakes.
Pygopods also have hind flaps of varying sizes but they are always present and clearly visible and are located beside the vent.
I hope this helps you tell the difference between Pygopods and Elapids in future.