Seriously, I think you're both too young, and if there's not some common point of interest (like, you both play WOW, or something) you'll be bored when you're alone.
But, if you persist in doing something, anything will do, trust me. At the age of 13, she's just insecure as you are. Act like you know what you're doing, even if you don't. She doesn't know what she would like you to do, so it's all the same. Don't talk too much, suggest some activity, it doesn't matter what, biking, arcade, mall, computer games, watching movies, swimming... You know what girls your age like to do.
I presume there are at least a few kids your age where you live and that you hang out with them sometimes. The next time you kids get together to do whatever you do, just go over to her house, ring the bell and ask her if she would like to hang out with you and your friends, 'cause you know she's just moved here, she doesn't know anybody blah, blah, blah. She should jump at the opportunity to meet kids her age. That's a good ice breaker and after that, if it goes well, you can invite her to do something together, just the two of you.
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