Answer:
No, the Cheshire Cat is a cat.
The only things in the kitchen that did not sneeze, were the cook, and a large cat which was sitting on the hearth and grinning from ear to ear.
`Please would you tell me,' said Alice, a little timidly, for she was not quite sure whether it was good manners for her to speak first, `why your cat grins like that?'
`It's a Cheshire cat,' said the Duchess, `and that's why. Pig!'
She said the last word with such sudden violence that Alice quite jumped; but she saw in another moment that it was addressed to the baby, and not to her, so she took courage, and went on again:--
`I didn't know that Cheshire cats always grinned; in fact, I didn't know that cats COULD grin.'
`They all can,' said the Duchess; `and most of 'em do.'