Your not supposed to pick them up or move them
I have heard that with human smell on them that the does will sometimes reject them.
This is a myth. The biggest problem with handling or "scenting" a fawn is that you are exposing it to predators by making it possible for something else to smell it. Fawns are "scent free" as the doe will lick it clean until it is... for a defense mechanism. They also will lay perfectly still for about the first 3 days of life or so. This leads people to believe that they are "abandoned" and will pick them up and try to rescue them, when actually, the mother is usually near by and will return to them. If the doe smells anything on the fawn, she will clean it again.
edit: I'm not busting anybody's chops for handling a fawn I literally handle hundreds of them each year ear tagging them, I just wanted to share a couple of facts. Next time you have the opportunity to pick one up, smell it... its crazy how they have ZERO scent. a piece of paper has more scent that they do!!