Think you will have to apply for a 'Validation Permit' to fly a NZ reg aircraft on your Oz licence plus you would have to complete a BFR once here (CAA requirement as part of the Validation Permit'. Application forms can be found on the NZCAA website somewhere. If you are only going to do the one flight it would probably be cheaper and easier just to hire a dual flight (instructor) where you get to fly and also with someone who knows the area and local conditions. Its not a forgiving part of the country if the weather turns.