As odd as it may sound, I think that a female would actually have the best chance as QB.
Short of a kicker, the QB is offered the best protection both by the line and by the rules of any player on the team. A QB really doesn't have to rely on sheer speed (look at Brunell, Bledsoe, Brees, ect) to play that position, and they also don't have to be the strongest guy on team. Obviously they still have to take a hit, but women actually have better "core" pain tolerence than men do. That's where a lot of QB's take their hits. Men on the other hand have better extremity pain tolerence (arms, legs, hands, ect).
If you were to take some of the taller, more athletic players in the WNBA and raise them from the start to throw a football instead of shoot a basketball, they probably could perform quite well in those roles.
It's just not something that anyone really thinks about.