Whoaaa....
Obviously this decision is completely up to you. But I'm a little concerned about the lack of time you two have had to build a good foundation for marriage. Having a great time for 2 months isn't a good reason to get married. Maybe there are other reasons you think this is a good idea, and you just haven't happened to mention them.
So here's some stuff that I think you both should have worked out before proposing:
- what are her faults? How might these affect you when living together? (eg. I get majorly grouchy and irrational when I'm tired or my blood sugar is low... and am liable to yell first and think later. This, uncontrolled, would be absolute hell on my poor husband. It's not fun for him as it is - and I do a LOT of work to stop it from happening)
- what are your faults? How might they affect her when you're living together? (eg. if you're impetuous and tend to buy things you don't need... this could cause major problems when you have kids and a tight budget... it's a tough habit to break and you should break it before you get married.. and have controls in place after marriage so it's hard to break the budget)
- what values do you hold which are important to you? How about hers? Do they match up OK? Don't just say yes unless you've specifically talked about it.
- what do each of you expect out of marriage? eg. does she want to be a stay-at-home mum? do you want her to keep working until you have children? Who will do the housework? How will you share out tasks that need to be done around the home?
- what's your basic personality type? What's hers? How do you plan to deal with personality conflicts (they WILL occur)?
- how do you deal with conflict with people that you're NOT feeling lovey-dovey about? How does she deal with conflict? If you can't sit down and rationally talk through conflicts with other people, you may find it extremely difficult when you're looking at her and thinking you'd rather be in a room with ANYONE else at that exact moment (that's pretty inevitable, too). Have you heard of active listening? Do you know how to check that what you heard was actually what the person meant?
- how do you deal with criticism? how does she deal with criticism? Do you get defensive and/or angry? Do you decide you're the worst person who ever lived and go into emotional meltdown? Or do you consider the criticism prayerfully, talk to others to get their opinions on the topic, then decide whether or not it was fair criticism, and what to do about it? And how do you both deal with criticism of your relationship?
- do you talk to other Christians to get their viewpoints on how you might be conducting your relationship better? Do you have a mentor? Or an accountability partner? Are you actively seeking spiritual growth? Is she?
- what church(es) do you both go to? Are you in accord about which church you'd both attend after getting married?
- do your callings match? eg. if she feels called to be a brain surgeon in San Francisco, and you feel called to be a missionary in Zimbabwe, your callings (or what you understand to be your callings) are mismatched and need further consideration.
- when you say that 'God tells me to do it sooner than later' ... how do you know? How have you checked this? Have you asked others (preferably older christians) to pray about this and tell you what they think God's saying? Have you asked advice from couples you admire?
There's a great book called Boundaries in Dating (Boundaries Before Marriage in some countries) by Drs Cloud and Townsend. That's where I got a lot of this material... oh, and personal experience

I'd really recommend getting hold of it and having a thorough read... preferably WITH your gf.
Hope this helps. GOd bless!