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If you can't get her to go out with you and get to know you I really don't know what you can do. She has to be willing to give you a chance or else you need to come up with some way to catch her...

Maybe send her an ecard --but nothing serious
Maybe a funny friendship ecard or something humorous (not the typical email forwards)
But video type things from YouTube

Proposing would either...

How old is she?
What do you mean propose?
You barely know each other

Can you communicate with her on the internet.

I take it you are young and that is common to not have anything to talk about.
Do you ever ask her why she won't come out and meet you. What does she say?
Maybe her parents won't let her or you...

Sometimes just being with each other and feeling comfortable with each other is all that is needed. Like watching a sunset or a walk on the beach ---who needs words.

Ask her questions like what are her hobbies, her likes and dislikes, where she likes to go and what she likes to do. When you ask questions you find out what you have in common and can find things to...