Is it normal to have a crush on somebody younger?

I'm a 23 year old male. I started talking to this girl whom I thought was around my age because of how mature she acted and looked. I was almost in doubt that she was only going to be thirteen in a few months. I didn't see much wrong with just being friends with her, because I feel like as friends me and her (surprisingly) have a lot in common. I know how young she is but because of how amazing her personality is and how mature she looks, I can't help but feel like I have a innocent crush on her. I wouldn't ever act on it, and I don't have any sexual urges or desires, because I'm not a pedophile, but is this normal?