I have to agree with The Exception here.
An ex of mine (not engaged, but cohabiting for 18months-2years) went on holiday to NZ with family, stayed with family friends for like 3 weeks. Almost exactly the same sitch actually
Anyway long story short, our relationship had been a bit rocky at the time of her traveling; hence she actually started a second 'relationship' with a guy there! Pretty ridiculous when you think about it, as we were living 24hrs travel time from NZ at the time; but that is women, sometimes; purely ridiculous, to the point of oblivion.
I only found out weeks after her return when she started calling the guy when I was in the next room.
Anyway, without wanting to p*ss all over your engagement bonfire, please do not be so naive to think that there isn't at least a small chance of something happening.
Ask yourself how happy you think she is in your engagement. Whatever you do, do not ask her. And whatever you do, f*ck her the best you ever have the night before she leaves. Like an orgasm she will not forget for at least a month, preferably more than once. That's all I got.
As far as passing the time goes; use your imagination.
In fact make the most of your month of freedom. Go out and make out with other chicks, make sure you're ready to marry this bird.
To be honest, it's probably make or break for your current relationship.
Hope it works out for the best