Your approach of starting a relationship implicit is not wrong. You do not get a relationship by declaration, because you can not declare feelings / attraction...
But you can declare your relationship as official, telling your family, friends, stranges who ask, that you are in a relationship. This leads to several possibilities:
You can ask her how she views the relationship of you ("Do you consider us as a couple?"). I did that myself with my current girlfriend and it worked. However this is not really romantic, so if she is a romance girl, I would not do it. There is also an advantage if she says no, because there is no rejection which can make things akward. But if she is shy, she might be afraid of saying "I think we are a couple.", although she wants to be one.
Ask her if she wants to be your girlfriend ("Do you want to be my girlfriend?"). This is more romantic, considering her being young, it is a suitable approach in my opinion.
Tell her that you see her and you as a couple. ("I think we can call ourselfs boyfriend and girlfriend!").
This is not romantic aswell, but makes it easier for her to agree, in comparison with the first suggestion.
You should also consider the surroundings while asking, if she likes romance, you can ask her after a nice dinner (or what ever she considers romantic e.g. bring flowers). If both of you are not so much into romance just ask her during a date at home.
Most important point is, to do it in a way, which suits your personality!
"Willst du mit mir gehen?" is a expression, which is more for teens (in my opinion and regarding experience with friends). "Willst du meine Freundin sein?" or "Willst du mir mir zusammen sein?" would be more suitable I think.
PS.: Good Luck :)