Okay. Again, I may be telling you something you already know, but you don't need that variation of travel conditions at the outset before you travel.
You can travel to, live, and work in NZ without restriction on an Australian PR visa, as long as you are of good character.
https://www.immigration.govt.nz/new-...-resident-visa It's if you want to leave and come back again, without having to start over once more on qualifying for NZ PR, that you have to get the variation of travel conditions.
You can only apply for this visa when you arrive in New Zealand – you can’t apply for it before you travel.
If you leave New Zealand your resident visa will expire - you can apply for a variation of travel conditions to allow you travel without affecting your New Zealand residence status.