NZ school terms run from January to December. I expect she would be able to go on a student visa, but how this would fair I dont really know. I'm not sure whether children of her age can go on exchange terms or not. Probably your best bet would be to contact a school close to your friends in Christchurch to see if they would accept her, and then speak directly with immigration to see if a student visa is the way to go.

I'm sure if it is acceptable it would be an excellent opportunity for her, so we wish you luck!