They are getting seriously beat up in the global economic mess (US$1 = NZ$2, roughly as of this moment), and experienced one of the most highest migrations ever last year, with a total of 48000 Kiwis leaving the country for Australia, and only 13000 returning.
Those numbers may not mean much in US terms, but the entire population of New Zealand at 4.26 million is less than the population of the state of Wisconsin (5.6 million), slightly less than the population of Metro Sydney (4.3 million), and significantly smaller than the city of Toronto proper (6.5 million). They can’t afford to lose too many people.
I am not being all that flip when I suggest it, but if the Key government (centre-right, and a bit nicer than Harpie up in Canada) is keen to make NZ grow, then they should seriously start courting LGBT migrants.
Currently, New Zealand does not allow for same-sex marriage (they have civil unions which are very close to marriage), nor do they allow for same-sex couples to adopt as a couple (only as individuals and with a prohibition of men adopting female children).
If New Zealand would be willing to address these two issues , and really play it up in the global media, then I think it would certainly help not just stem the brain drain, but also create a brain gain.
I also suspect that New Zealand could enact these policies much quicker than Australia (and considerably faster than the US*).
* Hey, we only decriminalised sodomy in 2003. Australia decriminalised it in (nationwide) in 1994 (although it took Tasmania 3 years to catch up). New Zealand decriminalised it in 1986.