Martingale can warp neck muscles
First let me say that you have a really nice seat on that horse, really, and your letting her run with her head up where she wants to put it is not so out of place for the time being. She is still very young, so contact is something that comes AFTER moving forward with good rythm and relaxation. A young horse needs to move freely at first, and your job is to stay balanced over her and let her find her own balance. Little by little, you will work with more contact such that she learns to accept and GIVE to the contact. However, most important is not losing the forward movement and not just dragging her down in front, as a Martingale can do. A lot of other folks said to take dressage lessons and focus on getting her to work from behind into soft contact. Both can be developed at the same time; working her into contact (and you will have to be more active in that, not just a passive passenger) AND encouraging her to move briskly forward from pushing hind legs.
The thing about Martingales, especially for ayoung horse, is that if they fight them and learn to brace against the incessant resisitance they will build muscles in all the wrong places on their necks. Once this habit is formed, it's hard to undo. I know Martingales are used for jumping but I think that is for a different purpose and are more a safety issue, no?
(obviously, I am not a jumping person)