I’ve got Aus RN registration through Trans Tasman from NZ and now working in Australia applying 189 RSMS. It seemed that you haven’t got registration which restricts you you work in Australia as a nurse. Both countries NZ and Aus nursing councils need ENGLISH test score 7 or B to apply for the registration. If you are British, I think you don’t need any English test. Just have to send a paperwork to NZ nursing council and then wait. You don’t even need to go to NZ. After that go for trans tasman application. I knew an UK RN who got Australia registration in a very short time via this way.