I'm sure you didn't do anything to lead her on. But it is fairly common for younger girls to have crushes on older guys -- even teachers.
You sound like a nice guy who doesn't want to hurt this girl's feelings. Nor do you want to be accused of something you didn't do.
Of course, there's no way for either of us to know if she is rational or a bit strange. So, there's no way we can tell if she will get weird if you tell her that you and she can't date.
However, I think you have to be kind to her, but at the same time be straight with her about the two of you not being able to date.
If she is asking you to go out, then you should tell her that you think she is a really nice girl, however, you are sure she would find you boring because your interests are probably so different from hers. Besides that, since you are sure she comes from a good family you are equally sure that her parents would not let her date someone so much older than she is. It is better for her at this point to find a boyfriend her own age, someone with whom she will have more in common.
I would suggest that you keep a journal and note the times and dates of all of your contacts with her. Just in case she ever threatens to accuse you of something. If there is any hint that she might, go to your parents and tell them what is going on. Then, contact the police to say that this girl is making threats toward you. While you don't want to get her in trouble, you do need to protect yourself.
Best wishes,