Possible Clues:

• Either "Lady and the Tramp" antagonist
• Certain shorthair
• Pet from the 'old world'
• It eats mice, as arranged
• Iams awfully dry -- disturbing nosh for pet?
• Blue-eyed pet
• After a fashion, meet Cassia - she's a blue-eyed pet
• Feline -- Matisse fancifully captures one that's played up
• Feline introduced from east as mice reproduced
• Carnivore for whom siesta came unexpectedly