Hunting dog heading for big, big bird (6)
I believe the answer is:
beagle
'hunting dog' is the definition.
(beagle is a kind of hunting dog)
'heading for big big bird' is the wordplay.
'heading for' suggests taking the first letters.
'big bird' becomes 'eagle'.
The initial letter of 'big' is 'b'.
'b'+'eagle'='BEAGLE'
(Other definitions for beagle that I've seen before include "Small short-legged hound" , "Short-haired dog" , "5 [MANS BEST FRIEND]" , "hunting animal with smooth coat" , "Small, sturdy breed of hound" .)