Im hitting on a girl whose older than me?

These past couple of days, I met a 16 year old (I am 13) Brunette, Green Eyes, great personality and everything...Basically shes my dream girl. So we've been chatting, talking, going out, getting to know each other more etc...I would always compliment her, and she always wished I was older, so she can go out with me, cause most of her Ex-Boyfriends we're real Jerks. She also loved my country (Italy) and the way I complimented her. I'm taller than her, I'm as fit as the other 16-18 teenagers and I'm more mature than the other guys in my class. Most of the time she would pretend I was her boyfriend in front of boys she never liked or boys who would flirt with her. Tomorrow she's going to Canada for good. Well I'll cut to the chase: Ive been hitting on a girl older than me (Which never happened to me) who is also hitting on me. But we both know that we shouldn't start a relationship because it would look real stupid. And i've been kind of "Depressed" because of this. Why must all good things come to end? >.< What do I do? (Like I said before Im taller than her, as tall as an 18 year old, and im in good shape) Thanks. >.<