So here's an update:
I got to Qatar and we talked about once or twice a week. That was fine, especially considering that the semester went into full swing. She works full-time in addition to a full load of classes so I was grateful that she found the time. I also called her via Skype on occasion, although that was rare because there's an 8-hour time difference. The emails from her gradually became more infrequent and then I didn't hear anything for two weeks. Before you think it, I didn't bombard her with emails or anything like that. When she didn't respond to the last couple emails I stopped because I'm not desperate. I was just about to tell her it wasn't going to work. I sent her a final quick "hi, how are you?" before that, however, and she responded.
Before I left, we'd established that we were both talking with other matches (remember, we met on a dating site). We'd both agreed that we could date other people while I was away so long as we kept talking with each other. She apologized for the gaps in communication but said that she's been extremely busy. Also, she's been exclusive with somebody and "it just sorta happened." She wants to pursue a relationship with him but also wants to remain friends with me. He's an Army officer and is being transferred away in March, but she wants to see what happens until then. From her email, it looks like she's been dating him for a while. I wasn't upset because she's dating somebody else (I'm considering a couple Canadian girls here), but that she kept me in the dark until it was too late for me to do anything. If the situation was reversed, I'd definitely tell her as soon as things progressed with a girl. She was also definitely not too busy because she found time to start an exclusive relationship. Anyways, I said there wasn't any way we could have a friendship right now because of the reasons I mentioned. That started an exhausting fight. She wants me to reconsider and we're both taking a couple days to think it through.
Experience has taught me that "I hope we can be friends" is often Womanese for "I can't see you anymore, but I'm offering a sham friendship so I won't have to feel guilty." I'm still inclined to refuse a friendship with her. Do you all think I'm being unfair or not?