Is it weird for the girlfriend to drive the boyfriend around on dates and stuff, since the boyfriend can't?

Oh, honey, not at all! Forget about every male/female stereotype you have ever heard and have yourselves a wonderful time!

I don't see anything wrong with it.

I dated a guy who couldn't drive yet, and you know what it didn't bother me 'cuz I liked him that much. :) Soo if she feels the same about you, she's not gonna care you can't drive.

No..If she doesn't mind to do so..

Help her pay for the gas XP

No, don't be so sexist.
Ok just kidding, nah, she drives, you don't, logic tells us all that its better for her to drive than you both getting on a musty bus.
If it bothers you that much then ask her if it bothers her because you feel like it should be you taking her, ask if she would prefer to leave the car at home and you pay for a taxi instead.
I think you will find she doesn't even think twice about it.

no it's normal dude, that's getting about the average these days :P