Agree that Carter is not captaincy material - and the same goes for Fat Cat. Both are larrikins, and teams that don't have them are the poorer for it, but they are not usually captains.
As I have mentioned before: McCutcheon is probably the most natural captain, but his place in the side is not assured, and nor is Mumm's. Fitzpatrick is another natural, but is not in the picture at all.
Elsom is a possibility, and how could he not be, since he has captained the Wallabies, but he probably has to concentrate on getting his mojo back as a player first. Vickerman is a player with gravitas and players listen to him, but you don't want somebody of his age taking over the captaincy reins.
Some of the others have captained in club matches but Barnes is probably not only the best candidate, but also the only real one. Elsom or Vickerman could be skipper if he misses a game.