I would endorse Nigels advice about renting or buying, and bike size and speed enforcment - on the button.
However, allocate your time in favour of the South Island - it has the pick of everything any visitor could want, the roads are better and less populated, the scenery is better, the people are friendlier (he says, ducking for cover
) - you'll love it.
You've also picked the best time possible for weather as well, so you can't go wrong.
If you still haven't made up your mind about a bike by the time you get to Dunedin, look me up - I'm sure something could be sorted.
V-strom 650, Transalp 650, DR-Z250