It makes absolutely 100% sense that it's a rabbit! Great find Lyric! Maybe a 40's version of Bugs Bunny?
Pretty certain its Brer rabbit prior to Disney doing a movie.
Found this post war edition cover art that has me thinking on a couple of points the face design and head position is very close to the nose art.
Outside of the ears of course.
The hand holding the umbrella never quite made sense however if it was a bowler hat like the book cover it would be Brer holding the rim of the hat and not a umbrella handle.