I guess she could be different in person than on other modes of communication.. but it kinda changes from person to person. Some people are very different, some are nearly the same.
5-6 hours is not impossible. In fact, it's very doable. I have met quite a few people who have met their wife/husband very far away. It's starting to happen a lot more than it used to, and I'm really seeing it as a "realistic" possibility.
Apparently, the only way it would end up working is if eventually you two go to the same place (you move there, she moves to where you live, or something else)... but, that DOES happen, and it happens a lot more than you think.
Don't think of your question the way you asked it. Ask yourself, 'do I like this girl?'. Don't be owned by what society says about relationships. Answer the questions yourself, make your own guidelines. Even if everybody here says you can't like someone you've never met, it doesn't mean that YOU can't. They can't answer that question because they are different people, and they all have different reasons for thinking what they think (myself included).
So, at that, what happens if we all say that you can't like someone you've never met? Give up on it... despite the fact that you said that "I don't know why but I like this girl very much"? Haven't you just answered your own question?
If a dream comes true... then is it still a dream?