Thank you for your question. Yes, New Zealand is mentioned in the Australian Constitution.
The colony of New Zealand participated in the early federation conferences. However, there was not strong interest in joining with the Australian colonies to form a new country. New Zealand delegates did not attend the conferences where the draft Australian Constitution was written.
The Constitution gives New Zealand the option to join Australia. Covering clause 6 of the Constitution states New Zealand may be admitted into Australia as a state. New Zealand has not yet taken up the offer. As non-Australian citizens, New Zealanders cannot vote in Australian elections.