I need some advice on my relationship?

So I went to Mexico in December 2010 and I met this girl and come to realize she loves me a lot. She told me that she fell in love me with year before in December 2009. But I didn't know she was into me until she told me in 2010. So we started hanging out and talked and talked about our lives and come to relize I fell in love with here and I think she is the one girl of my dreams and this is my first tru relationship. Is that possible? She says that I am the "one" too man of her dreams. So we became boy/girlfriend for a month close now I have returned to the USA and it is hard for long distance relationship but I call every weekend and send email. We have known and been in relationship for one month now. She tells me that not to find someone else and I don't want to find someone else. I even promised. She tells me that I am the one, in love with, she doesn't want me to leave her. And i feel the same She my question is any advice on how to tell her or show her I do truly love her and she can feel secure about i am truly the one for her and I am not going to leave her for someone else. Also any other long distance advice is welcomed. Because this is my first true relationship I have had with a girl plus it is a long distance one