Kind of fat, pet (5)

I believe the answer is:

puppy

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'pet' is the definition.
(I know that puppy is a type of dog)

I cannot understand how the rest of the clue works.

(Other definitions for puppy that I've seen before include "Young canine" , "Young animal" , "Whelp" , "Young dog" .)

I've seen this clue in the Evening Standard.

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