Roboto you overestimate my “support system.” Since I moved back to KC, I haven’t made too many new friends and my old friends from high school are married with children so they don’t get out much (read: at all). Though, I do miss some “alone time” which I’ll be getting this weekend since she is going out of town for a badminton thing.
Just to chime in: I proposed to my wife two weeks to the day after our first date, and less than four weeks after we first met. That was eighteen-and-a-half years ago.
No doubt this is the exception rather than the rule. But it’s worked (so far!) for us …
It’s moving faster than I’d be comfortable with. Purchasing furniture for someone I’ve been dating for a month? No thanks, but then I’ve been in a long-distance relationship for going on 3 years, so obviously everyone’s mileage varies. I certainly don’t have to worry about anyone moving in too soon 
Really, if you’re cool with it and aren’t just getting shoved into a situation you don’t like, then go for it, man. You (and her) are the only one that knows what’s right for you.
ETA: I would advise against rushing into this because you lack a support system elsewhere. If you’re looking to get serious with this gal just because she’s there, I’m not sure it’ll work out well.