An animal and one dicky bird! (6)
I believe the answer is:
pigeon
'bird' is the definition.
(type of bird)
'an animal and one dicky' is the wordplay.
'an animal' becomes 'pig' (pigs are animals).
'and' says to put letters next to each other.
'dicky' indicates an anagram (dicky can mean ill or non-functioning).
'one' is an anagram of 'eon'.
'pig'+'eon'='PIGEON'
(Other definitions for pigeon that I've seen before include "Short-legged bird" , "Baby" , "Seed-eating bird" , "Common dove" , "See 1 Across" .)