She's coming on too strong too soon. What do I do?

I recently started seeing this girl, who is fun, bubbly, y, etc. However, she seems to be coming on way too strong, too soon. I can't really gage how smart she is either. I've only been hanging out with her here and there for a few weeks and already she's gone from wanting to be "friends" to dating, from calling me "hey, you" to pet names like baby. She always says I'm adorable and all this other stuff, but I feel it's only right for pillow talk, not for texts, or PDA.(public displays of affection, not the personal digital istant) I'm a believer in love and that people have more compatibility than they know about, but I'm worried that she's a little immature and is making romantic decisions other than realistic ones. I've been nothing, but honest with her about how I'm not ready for a relationship and how I have certain fears. I told her I'd like to have something a little more grown up, but I don't know how vast her understanding of love really is. Even though she's my age, I think she still enjoys the more "movie" version of love. I don't disagree with the romantic things people can do together to invoke those feelings; however, I think I'm over high school. I don't want to break her heart by telling her that she's confused about love or whatever, because she's a sweetheart, but I don't know if I can let myself fall in love with someone who I think may be a pitfall. Am I up s### creek? Do I need to just grow a pair? Or is there something I can I do to let her know what's bugging me without really offending her? Please, help!