Throughout Beck's Song Reader, Beck sprinkled fragments and melodies and titles, to make the whole collection feel more complete and authentic.
One of the melodies is called "Zoological Garden," a short piano instrumental (I'm unclear if it's a fragment or complete) "sure to sooth the savage beast."
The art also states the song was "mainly composed" by Edwin Barnhouse. A lot of the names in Song Reader art are made up, or references to real people. It appears to me that Barnhouse is a reference to an ancient (but still going!) sheet music publisher, the C.L. Barnhouse Publishing Company.
I should also note that the title of this piece seems to actually be "Animal Kingdom" (and some people have covered it under that name). Zoological Garden looks to be the name of the made-up album that "features" "Animal Kingdom," not vice versa. However, Beck has copyrighted the melody in real life under the name "Zoological Garden," so I'm using that here.
That said, the artwork comes from an 1877 sheet music/song called "Zoological Garden," which you can see above and can be found here
. The art is borrowed, but the melody is Beck & Edwin's own.