Tabitha is a very furry dog who appears in File Under: 13 Suspicious Incidents, in the ninth incident, "Midnight Demon."
Midnight Demon/Panicked Feet
Tabby lives in Stain'd-by-the-Sea with the Cozy family- Thomasina, Tatiana and Treacle- and seems to spend most of her time asleep in her basket. After pretending to be his sister, Treacle hides his wig underneath her, but Snicket reveals it by calling for her, which prompts the dog to stand up and go to him for attention.
Snicket describes Tabby as a cozy, furry dog, and so fluffy that it is hard to tell her head from her tail.