Don't get me wrong, I'm a Diablo addict for sure, but... my honest choice would be (and that's also what I did when I travel) to not play Diablo. I've waited for Diablo 3 for years, even bought a new computer in advance hoping I would get beta access. Nothing. Then Diablo 3 was released a week before I left on a 3 months internship... so I basically missed the first 3.5 months of Diablo 3 after release. Absolutely no regrets. Getting into a new culture (and especially enjoying the freetime activities with all the new friends you'll make there) trumps even your favorite video game. You will not remember S8 as much as you will your stay in down under when looking back in 20 years from now.
That being said, maybe you have your reason why you still want to play. I'd probably switch back and forth, there are good reasons for both: on EU you probably want to get the stash tab. But you'll have high latency and play during times when people are offline. On NA you have the chance to meet people from your new home and might in general have more people to play with. But since the AUS/NZ server is on the NA realm that might be a mixed bag. So yeah, my preference would be: 1) Not playing at all, 2) EU, 3) NA.