Carrying drink at home — gallons! (6)
I believe the answer is:
toting
'carrying' is the definition.
(toting is a kind of carrying)
'drink at home gallons' is the wordplay.
'drink' becomes 'tot' (a small alcoholic drink).
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'gallons' becomes 'g' (abbreviation).
'tot'+'in'+'g'='TOTING'
(Other definitions for toting that I've seen before include "Lugging" , "Carrying with difficulty" , "Heavily laden" .)