You know this actually does make sense. He's never been a ginger, but has always wanted to be. Poor old Doctor, that's what hair dye is for. In all seriousness, what if there's a real Doctor and he's actually a ginger.
"The only way to get rid of her is to send her into a parallel world from which she can never return; otherwise she would stay with the doctor forever. We can't get rid of Rose. So, lets send her parllel universe !