i flew from Perth to Melbourne and back withing 4 days at 36w, also had to "lie" about how far along i was (they didnt like anyone over 35w). i was just uncomfy (and i had to entertain an 18 month old for the trip too!!) Definitely get letter stating that you're ok to fly from dr, they can ask you for one. And drinks lots of water. I usually try to take a good book, to distract me. Makes the time pass quicker.

Good luck!!