They are a part of Australasia.
The colony of NZ was once part of the colony of NSW (A.H. McLintock (ed), An Encyclopaedia of New Zealand", 3 vols, Wellington, NZ:R.E. Owen, Government Printer, 1966, vol 3 p. 526.), so it is only fit and proper that all Australasians past, present and future be invited.
s6 of The Australian Constitution permits the inclusion of NZ as a state of the Commonwealth is they wish to be included in this great land.
"The States" shall mean such of the colonies of New South Wales, New Zealand, Queensland, Tasmania, Victoria, Western Australia, and South Australia, including the northern territory of South Australia, as for the time being are parts of the Commonwealth, and such colonies or territories as may be admitted into or established by the Commonwealth as States; and each of such parts of the Commonwealth shall be called "a State".
When you have a birthday party, you generally invite all your brothers and sisters, cousins, uncles and aunties. Our cousins across the ditch are no different.