I obtained my NZ nursing registration before I left the UK to come to NZ at the beginning of this year. If I remember rightly it only took a month or so to receive the registration. Once you have that you can apply for a 'certificate to practice' which is kind of like the UK's annual PREP requirements/registration. I havent obtained my cert to practice yet as I left the UK on maternity leave and dont intend to look for work for at least another year.
Hope this has helped a little and if I can be of any help please ask
I'm new to all this too as we've only been here since March 9th so I'm still finding my feet and researching stuff.