Domestic animal eats everything -- one's moved by fork-lift (6)
I believe the answer is:
pallet
'one's moved by fork-lift' is the definition.
'domestic animal eats everything' is the wordplay.
'domestic animal' becomes 'pet' (I've seen this before**).
'eats' indicates putting letters inside.
'everything' becomes 'all' (I've seen this before).
'pet' going around 'all' is 'PALLET'.
(Other definitions for pallet that I've seen before include "Goods-stacking platform" , "Crude bed, lifting platform" , "For mixing paint or moving goods" , "Mattress stuffed with straw" , "Tray for lifting and stacking goods" .)