It'd depend on when it was and whether we go with a draft or not. If we do, then I'd imagine that we send a fairly serious troop contribution, although I can't really see an ANZAC being reconstituted. The Kiwis would also send their troops and may institute a draft. On the naval front there'd certainly be a contribution, though again timeperiod would be an issue. We had the HMAS Melbourne until '82, which makes life a little interesting. The RAAF would contribute substantially to patrolling for ships and submarines, and potentially could be ramped up quite a bit - IIRC at the end of WW2 it was one of the largest in the world. I would imagine, though, that much of the RAAF and RAN, and RNZAF and RNZN, remain in the Pacific with some units in the Indian, to secure those areas. Probably only bombers and fighters to Europe, and not all of them at that.
It'd be an interesting one given that Australia pulled out of Vietnam after it became incredibly unpopular at home, while New Zealand never got involved. Given our locations it does seem likely that there'd be some crossover. I wonder if the local lefties might see this as reopening Vietnam or as something completely new?
Without a year, it's hard to say exactly what could happen - the ADF and the Australian political scene changed quite substantially between 1970 and 1990.