Thanks to all for replies.
I got some first hand experience on how non-finnish speaking childrens learn Finnish.
I met a kindergarten teacher who works in Helsinki and has seen many foreign kids in her group. She told me that for example a 3 years old boy from Brazil needed 3 months to learn Finnish so that he managed to communicate with other kids. After 6 months he spoke Finnish fluently.
So it seems that we will just find a way a place where she could be in contact with NZ kids and look how fast she catch up the English.