Dude. She's shy. She said you were her first date. Why in the world would you think of hitting the road? If she's being touchy that is usually a good sign she's interesting. When she put her head on your chest you probably should've gone for the kiss. She'd probably be really embarrassed to say, "Yes, you can kiss me" Maybe she's never kissed before?
Well she must just be shy, because other than that, it seems really obvious that she likes you.
Since you're her first date, she's surely just not experienced, so she's probably just nervous and doesn't really know what to do.
I figure that because I'm the same way lol, and that's the way I got around the guy I like. Even though I like him a lot, I avoided kissing him just because I was nervous. It just takes a lot of patience on your part; make sure she's comfortable around you and that she knows there's nothing to worry about.
Then I'd say, just go for it. Make the move on your own. And also, I think asking for a kiss makes it really awkward (especially if the girl is shy), so just wait for the right moment and give it a shot. I'm almost certain you won't be rejected. :]
Next time you're in a moment like that, don't ask, just go for it. It's cuter that way anyways. Maybe afterwards ask her if that was ok or if she liked it, but don't ask her whether or not she wants you to kiss her. If she's a shy inexperienced one, she's not going to give you a straight answer as you already know. :P
But in answer to your question, I definitely think she's into you. Don't be afraid to move things a tiny bit quicker if you want. If it starts feeling like a little too much for her, I'm pretty positive she will let you know and you can act accordingly. Until you get a for sure "No, I don't want this" from her, I'd say all systems are go.
She's probably into you, but she's just shy. I mean if you truly are her "first date" then she's like many other girls and is to shy to make the first movement towards you face. Its better to just move in for the kiss instead of asking, it makes less time for any akward moments and more time for seriously cute ones.
wow this sounds like me and my boyfriend like.. 4 months ago lol. I had been going out with him for like a month and he was my first boyfriend so I didn't really know how to kiss or anything because I was inexperienced.. anyways I seriously WAS into him so don't always think it's that. She's probably just nervous.