without resident book (hukou), the child can not apply for an ID.
without an ID, the child can not get a Chinese passport.
Without a passport, the child can not apply for NZ PR.
So, you need to get her resident book with the birth certificate, then apply for ID with the resident book, then apply for a passport with the ID, then apply for PR with the passport.
It would be so much easier to have a child born in NZ if the child is going to live in NZ.
Again, in order to get the child a resident book, you will have to check with the local authority what is needed, you might need to certify the marriage certificate as well, as the parents' names will be needed for the resident book.