Support for little dog (4,2)
I believe the answer is:
prop up
'support' is the definition.
(I know that prop up is a more specific form of the action support)
'for little dog' is the wordplay.
'for' becomes 'pro' (as in being 'pro' something).
'little dog' becomes 'pup' (short for puppy).
'pro'+'pup'='PROP UP'
(Other definitions for prop up that I've seen before include "Support" , "Give financial backing" , "Keep going" , "Underpin" .)