I seem to remember it being referenced as a kid's rhyme in the book, going for the creepy use of something innocent in a murderous context. Of course you can question how innocent it is in the first place, and the weird infantilisation/othering of black people evident in the rhyme and other aspects of empire culture like golliwogs, black & white minstrel shows etc would have come from the adult world and absorbed by the children. I don't think Christie was consciously trying to target black people with the title. However that unconsciousness is what racism hides behind, revealed by the defensiveness when people are challenged on it.

cheers,
I