To each their own, my friend. Though some may think you need your head checked, my parents got married two weeks after my dad got off his mission (they didn't know each other before--though I guess I must also admit it was during the Vietnam War and my dad had enlisted for the AF) and have been dating ever since. Two of my other friends also got engaged after dating two weeks. I'd say test the waters--if she's all about it, invite me to the wedding. If not, I probably wouldn't mention the whole, "I think I want to marry you" bit because she's probably run faster than a gazelle in heat. Good luck!
~A fan of 6 months AT LEAST