I think the only real question there is "do you want to be a doctor in NZ?" - if so, it would be advisable to study in NZ. Medicine is a profession where you should study in the country you intend to work, if at all possible. The NZ PGY1 (internship year) job-matching gives priority to those graduating from a NZ medical school.Various Otago med students tell me to go to Aus over Otago as their programs are better whilst some say stay in NZ because Aus students will be prioritised by Aus hospitals
As A1 pointed out, you can't get an Aus student loan, nor a NZ student loan, if you study medicine in Australia, and are therefore required to pay essentially the domestic tuition fee plus your own living costs. This means you (or at least your parents) will need deep pockets.
The conventional wisdom of MSO has been that New Zealanders should only study medicine in Australia if they have been turned down from NZ medical schools, are prepared to fork out quite a bit of money, and are okay with the possibility of having to stay and work in Australia for a number of years.
Side note: I don't think "their programs are better" (if true) actually counts for anything - all the accredited medical schools in Aus/NZ aim to make you a safe, competent intern (PGY1), and as far as I know, "which Aus/NZ med school you went to" doesn't really affect anything further down the line for specialty application etc.