Bird or animal turning on baby in nursery rhyme (4,7)
I believe the answer is:
reed bunting
'bird' is the definition.
(reed bunting is a kind of bird)
'animal turning on baby in nursery rhyme' is the wordplay.
'animal' becomes 'deer' (deer is a type of animal).
'turning' shows that the letters should be reversed in order.
'on baby in nursery rhyme' becomes 'bunting' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'deer' written backwards gives 'reed'.
'reed'+'bunting'='REED-BUNTING'
'or' is the link.
(Other definitions for reed bunting that I've seen before include "Bird of marshes and hedgerows" , "singer" , "Bird breeding in marshes" , "Bird, the male with black head and white collar" , "Flier" .)