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Fool of a dog working with chief (6-4)

Ross

I believe the answer is:

mutton-head

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'fool' is the definition.
Both the definition and answer are singular nouns.
Maybe they are linked in a way I don't understand?

'a dog working with chief' is the wordplay.
'a dog' becomes 'mutt' (mutt is a kind of dog).
'working' becomes 'on' (on can mean working or activated).
'with chief' becomes 'head' (synonyms. I am not sure about the 'with' bit.).
'mutt'+'on'+'head'='MUTTON-HEAD'

'of' acts as a link.

Can you help me to learn more?

(Another definition for mutton-head that I've seen is " Idiot -- haunted Tom (anag)".)

I've seen this clue in the Sydney Morning Herald.
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