You should qualify for a 1 year
working holiday visa which I believe lets you work as much or as little as you want as long as you don't take up "permanent" employment somewhere. There is a lot of seasonal work in
New Zealand (farm and agricultural work and the like) or get a temp office job or work in a bar or something like that. Like Oz, New Zealand has a good backpacker culture and you'd find there are a lot of opportunities to do a bit of work and a bit of travel.