"Okay, well. We'll find you somewhere safe then." Dean wasn't looking to play babysitter, or nursemaid. Maybe the girl was tougher than she seemed right then, and could take care of herself. But he'd just saved her life, which sort of made him responsible for it by default.
"You ever fired a gun?" He'd get her somewhere safe, or at least relatively safe, and give her a gun. He had three. He probably shouldn't spare one, and he really had no way of knowing she wouldn't shoot him in the back of the head if he tried to dump her off somewhere, but he just might have to take the chance. He couldn't dump her somewhere unarmed.
"Using a gun to kill a zombie isn't the most effective. You have to blow the brains out, literally. That's the only way to kill the fuckers."