It is possible that this girl might not know what Skype is or its full functionality.
It is probably good to keep things warm and ask if she does IM or uses some other form of online communication (e.g. AOL messenger, or ICQ or other system). Perhaps the key is to explain that you are hoping to communicate and get to know her a little more and Skype or some other system might be a good way. You can even promise that you won't take up too much of her time and it would go only 5 minutes the first time around.