If it's what you want to do, then go for it! My DH and me met in Sept 2005, lived together by Nov 2005, got engaged in Feb 2006, and married 1 yr to our first date in Sept 2006. We did things quick style, but it worked for us. And here we are, almost 4 years from our wedding anniversary, happy as can be, and expecting our first baby. And if we can survive me almost dying, his mom passing away, my 2 grandmothers passing, and being really poor for the first 2 years together (literally, at one point we couldn't afford toilet tissue)....then I think we can survive anything. =)
Also wanted to add, my wedding was 13 days after my 20th birthday too!