Aww lovely cute scene! Interesting that you say 'Nanny Nay'. We say 'na-na-na-na-na' (or possibly 'nyer-nyer...') in a sing song sort of voice, same tune as 'Cry Baby Bunting'. We being northwest of England :)
*laughs* I suspect kids all over the world use variations of that taunt. Spelling will vary but it'll all sound the same!