Barber Shop in WotLK..?

Q u o t e:
Is the barber also going to be a plastic surgeon and/or eye replacement specialist?

Will I be able to fix my undead chin? It seems to be falling off...

You will be able to reattach your chin. The Barber Shops should have some spares lying about.

You can change anything that is an additional feature to the face but you can't change the face itself. There is no plastic surgery available. Luckily for the undead, this is considered a feature so it can be changed.