Woah, dude, you need to push that if you're a contractor. I'm ding a longer term role at the moment an charging $45 but only because they're happy for me to work 3 days and be left alone for the rest while I work on my startup. 16 is crazy! What skill set do you have? You are certainly worth more than that, even in NZ.
I was in your shoes a few years ago (in Auckland). Great experience if you're still learning, but get out of there as soon as you can. Auckland is terrible unless you're working remotely. There are much better opportunities down in Wellington or Christchurch.
Wow, I would have to say that seems completely unreasonable, even if you were in the smallest of towns in NZ. I don't know of anyone (inc. students) who charge less than $40/hour for development freelancing.