The Dormouse is a character in "A Mad Tea Party", often popularly known as "The Mad Hatter's Tea Party", Chapter VII  from Alice's Adventures in Wonderland by Lewis Carroll. He sat between the March Hare and the Mad Hatter. They were using him, while he slept, as a cushion when Alice arrrives,he slept in a cushion.
The Dormouse is always falling asleep during the scene, waking up every so often, for example to say:
`You might just as well say,' added the Dormouse, who seemed to be talking in his sleep, `that "I breathe when I sleep" is the same thing as "I sleep when I breathe!"
He also tells a story about three young girls who live in a treacle well, live on treacle, and draw pictures of things beginning with M, including mousetraps, memory and muchness.
Eventually the Mad Hatter and the March Hare put his head in a teapot. He later appears, equally sleepy, at the Knave of Hearts' trial and voices resentment at Alice for growing, and his last interaction with any character is his being "suppressed" (amongst other things) by the Queen for shouting out that tarts are made of treacle.