Well, i think it best if you come and go to dates in separate cars until you are serious. Otherwise things could go poorly and one of you would have to drive the other back. After that, i would say it doesn't really matter. Unless it is very formal, in which case the guy ought to drive.
I think it's okay for you to drive. Like if you you are the one planning the date. You need to use your car for storage space. Stuff like that is fine. Also I don't think you HAVE to wait till you are deeper in the relationship for you to drive.
Are you thinking that even if you use your car that he should drive it cause he is the man?