I spend several months a year without an internet connection when I have to be in the field in various African countries for work. It can get boring because there often really isn't anything to do in the evenings, except when I get to spend a couple of nights in one of the bigger cities, but I'm usually swamped with work when I'm there. I usually buy a cheap guitar and practice my playing while I'm there, or I work on my writing. It's very nice actually. Gives you a lot of time to put your life in perspective. Having the world and the people slow down so much around you is one of my favorite things about working in Africa for longer periods of time. The much bigger downside is that the food can get really bad for weeks at a time. I start missing good, varied meals more than the internet or tv shows. In fact, whenever I return I always avoid playing games or surfing the internet like a maniac for a couple of weeks. Just feels wrong. Of course, after a couple of weeks I'm back to my old habits. I think I'll keep doing it for the next couple of years.
Of course, living with slower internet isn't the big problem here. You get used to it, and it might even be nice. The real question you have to face is if you're willing to change your lifestyle that much (because of the new location more than the internet speed) for this girl, and if you're ready to actually live in the same house as her every day of your life. None of the answers to that question make you a bad person, but it's really important to talk with her about her future plans before you move in with her. Does she plan to live there for the next year? The next five years? Forever? Would she be willing to move for her/your work?
Gaf can't answer any of those questions, only a couple of good conversations with your girlfriend (and maybe some IRL friends who know you really well) can help you find the answers.