Possible Clues:

• Small British rodent
• Companion of the Mad Hatter
• Mad tea party dozer
• Place to rest by river for sleepy little creature
• Somnolent guest, could be awakened at a pinch
• Bedroom valueless for one falling asleep over tea
• Sleepy partygoer in the large bedroom by the river
• Carroll made the little beast go to sleep at tea
• Alice tea party creature
• Small, furry-tailed rodent