garry, too funny! Having raised a daughter I totally relate!
Ivlatt, I understand that you truly believe that you and this girl are right for each other but please remember that you are still very young and have many roads to travel before choosing your path. You mentioned that the two of you have some meaningful things in common, like rough childhoods, etc. Please, realize that AT YOUR AGE marriage can often be viewed as an escape from an unhappy home life and not what it should truly be...a lifetime commitment between two mature people who, knowing the difficulties they are facing, CHOOSE to face them together! You have been given some very good advice by other posters...visiting each other, looking into university, etc. Please give all of this the thoughtful deliberation it demands and don't rush into anything.
Good luck and please continue to discuss this all with adults that you trust...if not your parents then others...and of course, come to this forum if you are open to discussion that may not agree with you. Remember, support comes in all types of packages...just because someone doesn't think you're making the best choice, doesn't mean that they aren't supportive!