Circular shape? Staff carrying barrel with it to yard (9)

I believe the answer is:

rotundity

'circular shape?' is the definition.

'staff carrying barrel with it to yard' is the wordplay.
'staff' becomes 'rod' (I've seen this before).
'carrying' indicates putting letters inside.
'barrel with' becomes 'tun' (tun is a kind of barrel. I am not sure about the 'with' bit.**).
'to yard' becomes 'y'.
'rod' going around 'tun' is 'rotund'.
'rotund'+'it'+'y'='ROTUNDITY'

(Another definition for rotundity that I've seen is " Being plump".)

I've seen this clue in The Independent.

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