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' says the letters should be written in reverse.
'on baby in nursery rhyme' becomes 'bunting' (I can't justify this - if you can you should believe this answer much more).
'deer' in reverse letter order is 'reed'.
'reed'+'bunting'='REED-BUNTING'
'or' acts as a link.
Can you help me to learn more?
(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" .)