1. Grad School at that point is generally locked in, however, plans do change. Furthermore people who are making long-term plans around each other are capable of handling separation, and strengthening in it. You aren't in your parents house anymore, where where they move determines who you know and spend time with.
My wife and I were never co-located prior to a couple of months after we were married. Our entire relationship up to that point was distance; phone, skype, email, with me driving down over the weekends, etc. It wasn't ideal by any stretch of the imagination, but we were about your age at the time (I had just graduated and joined the Marines, she was still in college).
2. If you are making long term plans around each other at that point, its' not impossible you find a way to move there as well.
3. I'm not positive on what it means to open ones' heart because one is bored. If you honestly think she is looking to simply use and lose you, then, yeah, I wouldn't recommend that relationship under any circumstances. But if you aren't sure of that - I don't think the scheduled leave date is as big a hindrance as perhaps you do.