Jonathan Caws-Elwitt suggests that someone should write a book or paper entitled Double Talk: A Deep-Structure Analysis of Binary Repetition Patterns in Anthropomorphized Animal Imperatives within English-Language Juvenile Formulae. [For example]:
"Ladybug, ladybug [fly away home]"
"Pussycat, pussycat [where have you been]"
"Teddy bear, teddy bear [touch the ground]"