No not a good time to buy as the yields are so low, and capital values are stagnating/falling. However, as a long term investor the predicted increase in rents is always welcome.

As for the immigration stats, yes you are right about the trans tasman movement. However many of our immigrants come from the uk, South Africa, and Asia, so the loss to Australia is offset by these. NZ population is predicted to increase and peak at around 5 million so we have a bit of time to go yet. Plus like sydney, much of the population growth occurs in nodes which benefits the local property prices. There are always markets within markets always be suspicious of generalisations which grab attention. They sell newspapers and books.

The tax cuts you mention are interesting. When I lived there a couple of years ago there were a lot of hidden state taxes that tended to offset apparent federal tax reductions. My comparative net income in NZ was actually higher than oz. Also beware of the impact of tax cuts on inflation....