A small drink for doctor, overproof (4)

I believe the answer is:

drop

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'a small drink' is the definition.
(I've seen this before)

'doctor overproof' is the wordplay.
'doctor' becomes 'Dr' (abbreviation).
'overproof' becomes 'op' (I can't explain this - if you can you should believe this answer much more).
'dr'+'op'='DROP'

'for' is the link.

Can you help me to learn more?

(Other definitions for drop that I've seen before include "Desert" , "shed" , "Pendant earring" , "Discontinue -- delivery" , "Let fall" .)

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

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