Anywhere will hook you up with a position if you front up with the money. Most places insist they have an interview, but at the end of the day, unless you have serious issues, they'd love to take your money.
When choosing your location, do factor in the climate. It's a big move, moving from warm/mild winters in Perth to a very cool climate in Dunedin. Perhaps look at Tauranga (Bayflight) or Nelson (NAC) which both seem to be very good, equivalent options with a slightly warmer climate.
Edit: Forgot to add, as you have probably read, some places wont take you via NMIT because you are Australian. Kiwis first, everybody else second unless you're paying cash.