I'll do the obligatory warning:
Australia has a pretty massive oversupply of medical graduates. Right now, New Zealanders who study there are category one for internships. But by the time you'd graduate in 6 or so years time, it'd be entirely possible that New Zealanders studying in Aus could miss out on jobs to ensure all of the Australians get one. And NZ has oversupply issues of its own (last year it took a last-minute mad scrambe to ensure all domestic students got jobs), so it'd be pretty difficult to come home for PGY1 if you missed out in Australia. Even if you did get a PGY1 job over there, their training pipeline is more congested than ours further up as well.
So going to Australia to avoid the competitive first year entry at Otago/Auckland would be very much at your own risk.
Then there's the issue of paying for your study and the costs of living while you're over there. My understanding is that New Zealanders aren't eligible for an Australian student loan for the first few years, so you'd have to front up probably > $10,000 per year in course fees, buy all of your books/materials and cover all of your living costs. If your parents are super rich, that might not be an issue for you. But if not, you're going to have to find an awful lot of money from somewhere.
There are more comprehensive posts regarding the issues facing kiwis who are looking at going to Aussie for med (and I'd suggest finding and reading them), but those are the two biggest ones.
I would suggest that you'd be much better off trying for entry here (and if your academic grades and UMAT scores are good enough for Aus undergrad entry, you'd have a very good chance of getting in here). If you miss out here, then would be the time to start thinking about whether heading to Australia would be worth it for you.
Edit: Back when I applied to Otago during HSFY in 2011, I applied to a few Aussie schools as a back-up. Our GPA translates *very* favorably over there, so I got several interviews (and an offer at one school which didn't do interviews). I didn't have to go to any of the interviews in the end, but the point is that HSFY/OLY1 students are in a very good position to apply to Aussie schools, if you wanted to do that as a back-stop during first year.