Haven't looked at the NT to be honest haha. But it looks like they don't require permanent residence there.
I know from friends in Western Australia that it was not possible for them to get one and they were told to come back when they have PR .
When I first arrived in NSW the overseas visitor license was actually much more restricted, they were only valid for one year and you have to renew them every year (fees and paperwork) even though I was on a 5 year visa. When I left they changed that though.
You probably might still be able to get them in other states on a case by case basis its just that you are not supposed to get them and it was just one example of the stones they throw in your way when you are on a temporary visa.
Yes definitely recommend getting on Aussie PR as soon as possible. It would actually mean you could live in NZ as a resident with all the perks too so thats something to think about .