I've noticed that a lot of people get quite emotionally invested in on-line relationships, even to the point of feeling that they are in love, despite never having met the other person IRL. My main advice is that, until you have spent time in the physical presence of someone, you do not know that person. You may have the illusion that you know the person, but it is an illusion. You say you love her the way she is, but I would caution you that you don't know the way she is. You have never actually met her.

So go ahead and get to know her better, if you want to. But be prepared that you may discover that she is not who you think she is. Whatever problems you are picking up on, like her moodiness, will probably be bigger problems when you encounter them close up. Then you can better evaluate if this is someone you really want to get involved with. Also, she doesn't really know you yet. When she actually meets you, she may change a lot in how interested she is in you.