Play with lackey's little pooch (3,6)

I believe the answer is:

toy poodle

I'm a little stuck... Click here to teach me more about this clue!

'little pooch' is the definition.
The answer and definition can be both animals as well as being singular nouns.
Maybe there's an association between them I don't understand?

'play with lackey's' is the wordplay.
'play' becomes 'toy' (synonyms).
'with' says to put letters next to each other.
'lackey' becomes 'poodle' (I've seen this before).
'toy'+'poodle'='TOY POODLE'

Can you help me to learn more?

(Another definition for toy poodle that I've seen is " Miniature curly-haired dog".)

I've seen this clue in The Telegraph.

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