Q
",,, wondering about the origin of bunny ,,,"

A
"Alas, it’s not there largely because we don’t know. Bun was an English dialect word, recorded from the sixteenth century, which was used for a squirrel or rabbit. It seems that the word turned into the endearment bunny in the following century, and only later was it transferred back to the rabbit.
There is a suggestion that the word may have originally referred to the small tail of the rabbit, in the same way that a tight coil of hair at the back of the neck was also called a bun, because both were roughly the shape and size of the cake. Others argue that the origin was the Gaelic word bun that meant a stump or root, and which could refer to the tail of a hare.
But neither origin explains why it was applied to a squirrel, whose tail looks rather different. But then, we don’t know for sure where the word bun in the sense of the cake comes from either, so it’s all quite obscure."
https://www.worldwidewords.org/qa/qa-bun1.htm