Yeah, I'm sure you would quickly run into all kinds of copyright enforcement issues if you tried to distribute the stream, even if you did restrict it to NZ. However, there are services that do exactly this kind of thing internationally, like Filmon and Streema, so I'm not sure how that works.
I think they would only have a problem if I am earning money from there content. But if I'm not and it will all be free, I don't see why guys like TVNZ or Mediaworks will have a problem, it's just more eyes viewing there content at no cost to them, and i'm not getting money from it. I don't know, will see what happens, wanna see if it's possible to stream it first in the spare time.