Bearing in mind I'm a civillian oik with just a passing interest in these areas... I'm sure that idea has been studied.
In reality from the little I know there appears to be a fair bit of commonality already.
NZ procurement decisions have seemed to pretty much follow Australian ones same Frigates, same helicopter types (NH90, Seasprite), the knucks used to fly pretty much the same jets (Macchi, A4).
Detachment of 75 squadron used to be based in Nowra - see Spaz's earlier photos, flying attacks on RAN ships etc.
RNZAF do Antarctic support,
AFAIK RAAF do not.
Formal integration would be quite another step!
In reality, if anything went down, they'd probably function as a single self defence force anyway I'd imagine.
They've deployed together to places like Timor-Leste.
Someone else who knows more might be able to shed some light.