"Papa-Oom-Mow-Mow" is a 1962 novelty nonsensical doo-wop song by The Rivingtons. The song peaked at #48 on the Billboard Hot 100 and #35 on the Cashbox charts. The band released two similar follow-up songs over the next several months, "Mama-Oom-Mow-Mow (The Bird)" and "The Bird's the Word".
Anachronistic songs in Toobworld are nothing new. Dr. Miguelito Loveless and Antoinette sang "The Sloop John B" (or "The John B Sails") in "The Night Of The Raven" - that took place in the 1870's, but the folk song first appeared in a 1917 American novel, "Pieces of Eight", written by Richard Le Gallienne. (So it may trace even further back to the time of 'The Wild, Wild West'.)
Within the "reality" of Toobworld, perhaps the "Papa Oom Mow Mow" song started out as a native folk song from the island of Taratupa, and the crew brought it home after the war. There one of their neighborhood kids heard it and then used it when he grew up to become one of the Rivingtons......