Nanny's little one is Josh (3)
I believe the answer is:
kid
This clue is a triple definition!
'nanny's' is the first definition.
(thesaurus)
'little one' is the second definition.
(child)
'is josh' is the third definition.
(both can mean to joke around)
(Other definitions for kid that I've seen before include "Sort of glove" , "Tease; hoodwink" , "Pretend" , "Joke" , "Deceive - child" .)