Cute! How big does the face have to be? It looks like a series of balls: one large flattened for the face, 2 slightly flattened for the cheeks and a cone shape for the nose. 2 small white for the eyes or those could be piped on. The black could also be piped on. The fur also piped. It could be done with fondant or marzipan or even bc.
I think I would use fondant....but It looks as it bc could definately be used with out a problem. It would have to be stiff.
Im not exactly sure how I would do a beaver...but in my head right now Im picturing a 1/2 football pan for the body on a sheet cake with a big flattened tail. remember the tail has the pattern of a hm...um...."fence" I guess. (lol I was trying to think of something to compare the patteren to)
Then..with that head you received as a guide on the other end of the football.
Dont forget the big white buck teeth!! 
Maybe would be cute if on the sheetcake you made "sticks" with chocolate fondant for the dam, as well as water with some piping gel to make it shiny
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