Here's an extract from a short piece over at ihobo discussing the distinction between what we call an avatar, and the representational props that can be considered dolls (or models):
What is it that we call an avatar? How do we actually use this term, and are the things we tend to call avatars really the entity most deserving of this title? The term avatar, if it is to be deployed usefully, refers to the means by which the player of a game interacts with its fictional world. But in which case, the avatar as a representation is secondary to the avatar per se – surely the parser was the source of interaction in Colossal Cave Adventure, which after all did not represent the player at all... But if there need be no graphical representation for the avatar, then there is a distinction between the avatar as the source of interaction and the avatar as representation. The latter is merely a doll that prescribes we imagine how we appear in the fictional world, not that we are present in the fictional world.
You can read Avatar and Doll: Entering Fictional Worlds over on ihobo.com.