My girlfriend wants to get married soon, we're both still teenagers, what should I do?

Ok, I've been with my girlfriend for what is going to be 16 months very soon in a long-distance relationship. Recently, she made the very big decision to transfer into my school. This is a huge step, because originally she wanted to go to school in Hawaii. I've been putting in the miles to be sure that this relationship continues, refusing to believe that just because high school is over, we should part ways. As a term for her moving in with my as a junior in Fall 2012, she says that she wants us to be married. I'm very serious about this girl and I can easily see myself sharing the rest of my life with her. I have thought about proposing to her in the past, but it was mostly inarticulate romantic fantasies that never left the brainstorming stage. At this point in my life, I can vow that I will marry her, but I'm interested in making this work. There is no history of divorce in my family, it has always been until death do you part and I don't intend to break that trend. I want to get this right the first time, but I know that getting married before 21 does not feel like a stable way to start what will probably be the hugest life decision I will have made so far. I really want to be clear here, I am not trying to weasel my way out of marriage. The longest time that we've lived together, just the two of us, was 8 days. Granted, they were a fine series of days, but I need a little bit more than that to make such a huge commitment. I want to live with her in an apartment for a little bit, just to see if we have the compatibility to sustain a relationship in close quarters as well as over long distances. Am I fair to be hesitant? Is 20 too young to get married? What's the right thing to do here?