Flying while pregnant is one of those issues with a lot of "ifs". It's generally safe to fly while pregnant IF your pregnancy has been completely normal with no complications, you haven't had any symptoms of early labour or abnormal spotting, your blood pressure is okay, and you haven't had oedema. Short flights (like to Queenstown) you should be able to manage just fine right up to 36-ish weeks. Longer flights (like to the US) have associated risks, such as higher risk of blood clots/deep vein thrombosis, oedema, and other delightful yucky medical things.
At six months along, you should be in what I always called "the good zone" -- out of morning sickness but not quite into Braxton Hicks/intense discomfort. You should still be mobile and not *too* massive in size (nothing more fun than trying to strap yourself into an economy class seat when your bum is wider than the seat).
I would strongly recommend investing in some travel insurance. Many credit cards have travel insurance as a benefit if you book your tickets on the credit card (my DH's Amex card has this as a feature). I'd also have a contingency plan ready, knowing where the nearest hospital is located to where you're staying, and letting your midwife know that you're travelling, how far, and how long you'll be gone. I would also let the airline know, just in case. Better to prepare as much as you can. And if you're booking your tickets now-ish, I'd also just keep in mind that you won't know how you feel when you're pregnant until you're pregnant -- you may feel amazing, you may feel like crap. You may get pregnant with triplets (!!!) and on bedrest from 20 weeks.
This won't matter if you're staying in the country, but when I went to Singapore just before I got pregnant, I remember reading that if you're more than 6 months pregnant when you travel there, you had to take a medical note along and sign a statement saying that if your baby was born there, you wouldn't try to claim Singaporean citizenship. Different countries have different rules for stuff like that. Just food for thought!