Thank you, Joe, for mentioning the names and linking the Wikipedia articles. There we read clearly that both authors emigrated from the Russian Empire (now Belarus) directly to the USA (whereas many other Yiddish speakers stopped over in Germany or Austria between the respective revolutions).

The German lyrics are attributed to Heino Gaze, himself a composer of light music, but quite "Aryan", born in Halle, close enough to formerly Plattdeutsch-speaking areas to mistake "Ossen" for oxen, definitely un-Yiddish. The Hasenpfeffer theory seems possible to me, that is all I said. (Google-translate, though, translates Hasenpfeffer as קיניגל פעפער – "Kinigl fefer", the first word corresponding to German "Kaninchen" = rabbit. But then, Yiddish has its dialects and variants, and Google its idiosyncrasies.)

Like many songs by Manning, Gaze, and similar authors of that time, the lyrics can be seen as tongue-in-cheek or even "nonsense poetry", but its success and its declaration as a children's song indicate that many listeners took its tendency for face value.