Hi,
for postgrad training, you still need to get registration in NZ, but it is under a different scope of practice. The website of the NZ Physioboard has got really detailled information. Go to:
The Physiotherapy Board: Registration - Special Purpose
It sounds like it is easier to get this registration, before going for the full registration under general scope. But, ...?
I have had Indian colleagues, who got NZ registration, but it took quite a while and one of them had to do competency exams.
You are right about Trans-Tasman recognition. Once registered in NZ, you are elegiable to work in Australia. But you will still need to get registered and get a practicing certificate ($$$) from the state in Australia, in which you would like to work in .
Hope this helps,
Fyzzio