I beg you, don't propose to her because you want her to stay. For the sake of your relationship, just don't. If you love her, and I'm sure you do, let her go.
I did what your girlfriend is doing. I left 600 km away from my boyfriend and family last January for school. My boyfriend was and still is wonderful and he let me go. It has not hurt our relationship at all, I could even say that it has helped it it many ways because we both had things to live and things to learn on our own. I came back for the summer and this summer has been the best summer of my life.
It turns out I am very unhappy with the choice I made. I am very disappointed in the school and the program I study in. During the school term and with the summer job I had, I discovered something that is linked to my field of study and interests me even more. I looked for programs in that field of study and found one that seems absolutely fascinating... and it's back home!! So I am coming back next summer to stay. We started talking about moving together and getting married.
The reason I'm telling you all this is that you have to let her go, and who knows? She might come back sooner than you think. It'll be hard on both of you, but it could lead to great things. When she comes back (or the year before if you feel like it), then propose. It'll be worth the wait, I promise.