Children's character who says "It's not much of a tail, but I'm sort of attached to it" (6)
I believe the answer is:
eeyore
(Other definitions for eeyore that I've seen before include "A. A. Milne's eternal pessimist" , "donkey in wood" , "Miserable donkey" , "Milne's depressive donkey" , "A. A. Milne donkey" .)