New Zealand was granted Dominion status in 1907. The title Dominion means nothing significant, in British law and legislation the term was synonymous with colony. It wasn't until January l0, 1920, however that Australia became a sovereign nation in its own right when both Australia and New Zealand became foundation members of the League of Nations - the forerunner to the United Nations.

Membership of the League of Nation was restricted only to sovereign countries, and Article XX of the Covenant of the League of Nations required the extinguishment of any colonial laws applying to a member state pre-Sovereignty.

That meant the Constitution Acts in New Zealand and Australia passed prior to independence became legally void under international law.
It was a condition of membership of the League of Nations and later the United Nations.

But no new constitutions were ever forthcoming in either country.
It continues to be a founding principle of the United Nations charter, that the laws of one state cannot be used in another unless ratified by a mutual treaty.
...
The Australian Government, allegedly realising its difficult constitutional position, passed the Australia Act in to repeal a range of Imperial laws and shore up its status.

New Zealand, in the same boat as Australia, did likewise with the Constitution Act of 1986 and the Imperial Laws Application Act of 1988.

However ITR argues that both Acts are also void, as it is impossible under international law and the UN Charter for one nation to pass legislation repealing the laws of another nation. Nor are the Acts valid, if the government passing them is not.
...
New Zealand formally severed its colonial ties from Britain by ratifying the 1931 Statute of Westminster in ceremony on November 25, 1947. Britain again drafted a new Constitution for New Zealand, again passed in Westminster, authorising its colony to change any provisions of the old 1852 colonial constitution.

Except, as the Australian Government learnt at great cost, no laws passed by Britain are valid in New Zealand or Australia, nor have they been since 1920.