The cartoon is a commentary and satire of the food rationing that was happening in the USA during World War II.
At the end, as the buzzards prepare to eat the rabbit, the bunny holds up a sign stating it is "Meatless Tuesday", causing the buzzards to weep tears. Meatless Tuesday was originally implemented during World War I by President Woodrow Wilson. This was in addition to foregoing meat at one meal each day for the rest of the week. The United States Food Federation coined the terms "Meatless Tuesday" and "Wheatless Wednesday" to remind Americans to reduce their consumption of food products deemed critical to the war. This campaign was resumed during WWII when meat, and other commodities such as gasoline, rubber tires, and sugar were rationed. "Meatless Monday" is now an International effort to reduce the consumption of meat to help improve people's health as well as the health of the planet.
The gag about the characters envisioning each other as food was also used in the WB short "Wackiki Wabbit" which was released the same year.
While the character is credited as "Jimmy Durante Buzzard", he's never referred to by name. The other vulture, Joe, only addresses him as "Pal".
The film title sends up the 1943 musical, "What's Buzzin', Cousin?" which starred Ann Miller.