Hopefully you will find that you are over thinking it. I felt the same, and then I told my parents I had a boyfriend and they weren't at all weird about it, and turns out all the worrying had been for nothing.
Even if this doesn't happen, just tell them. You don't have to take her round there or anything, but it's better that you're not keeping it a secret. Also, if you do eventually take her round your house, then the sooner you tell your family about her the longer they will have to digest the information and hopefully they will be less weird when she does come round.