Would it not have made more sense for them to be a single nation? After all they are close together and are populated by the descendants of more or less the same people.
While not stifling further input, this response gives a succinct answer.
/u/LeftBehind83's link does give a succint answer. I wanted to add a few things.
Firstly, Australia wasn't a single country until Federation in 1901. Before that it was a combination of self-governing colonies and the crown colony of Western Australia. New Zealand also existed as a separate colony.
The argument that they ought to be a single country is about as logical as saying that Canada and the US should be a single country because of English settlement. It is an oversimplification of historical events. Australia exists as a federated commonwealth because the states voted to federate, New Zealand did not do so. That is the simple answer to your question.
New Zealand was indeed invited to join the Federation, and as pointed out in the linked thread is mentioned in the Constitution. However, this appears in Clause 6, under "definitions", and is qualified, as are the states, with "as for the time being are parts of the Commonwealth", which does not mean necessarily that NZ could join the Commonwealth without a referendum. That would be dealt with under Chapter 6 which deals with establishment or admission of new states.