When it's raining cats and dogs, don't step in one! (6)

I believe the answer is:

poodle

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'one' is the definition.
Although both the answer and definition are singular nouns, I cannot see how one could define the other.

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for poodle that I've seen before include "toady?" , "Looped around the dog" , "Pet dog; obsequious chap" , "Small dog" , "5 [MANS BEST FRIEND]" .)

I've seen this clue in the Evening Standard.

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