Budge led on; doctor hit with a baton (10)

I believe the answer is:

bludgeoned

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

'hit with a baton' is the definition.
I can't judge whether this defines the answer.

'budge led on doctor' is the wordplay.
'doctor' indicates an anagram.
'budge'+'led'+'on'='budgeledon'
'budgeledon' with letters rearranged gives 'BLUDGEONED'.

Can you help me to learn more?

(Other definitions for bludgeoned that I've seen before include "knocked out" , "Hit by stick" .)

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

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