Your child does not need to be enrolled in any school until s/he turns six.
A couple of months before this, in order to legally home educate, you need to contact the Ministry of Education to obtain an application for a "Certificate of Exemption" from the legal requirement that all children in NZ aged 6 to 16 be both enrolled and attending a registered school.
After six months of home educating with a Certificate of Exemption, you qualify for an annual "supervisory allowance" from the Ministry of $743 for the first child, $632 for the second, $521 for the third, and $372 for each one after that.
This is paid in two installments by direct credit to your bank account twice a year as long as you also sign a statutory declaration document sent to you by the MoE every six months affirming that you are still teaching the child(ren) "as regularly and well as in a registered school".
There may also be another check up on you in the form of a review of your home education programme by the Education Review Office (ERO), but not every home educator has this experience.

To apply for a Certificate of Exemption, contact the Ministry of Education.
(to find their phone number, look under "Education" in the blue section at the begining of your phone book)
 


Hear, my son, your father's instruction, and reject not your mother's teaching. -- Proverbs 1:8