Small child begins bassoon a bit young (4)

I believe the answer is:

baby

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

'begins bassoon a bit young' is the wordplay.
'begins' suggests taking the first letters.
'bit young' becomes 'by' (this might be a standard abbreviation I've not previously seen).
The initial letter of 'bassoon' is 'b'.
'b'+'a'+'by'='BABY'

Can you help me to learn more?

(Other definitions for baby that I've seen before include "Timid person; very small" , "personal project" , "about to howl?" , "Small child" , "Love" .)

I've seen this clue in The Irish Times.

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