The cartoon opens with the drunk stork talking to himself in the woods, while the gorilla baby he is supposed to deliver walks out of his bag. The stork is shocked to find that he has no baby to deliver. He has to find that new baby or he'll be kicked out of the Stork Club. Coincidentally, what scene should appear next... none other than Bugs Bunny, who is singing "I dream of Genie, she's a light brown hare..." while roasting a carrot not too far from him. The stork knocks him out with a stick and takes him to the gorilla house, as the new baby. The bag is closed and they are both excited, until they open the bag, which reveals Bugs. Elvis (the male gorilla) goes to get a club to hit Bugs with, but the mother (dubbed "MAMA!" throughout the episode) stops him. MAMA explains "no matter what he looks like, he's still your son!" Bugs Bunny awakens, and is not about to assume position of a baby gorilla, so he tries to get away, to which his gorilla mother responds with a spanking for trying to run away.
Elvis growls at Bugs when mother gorilla prompts him to "kiss your son". So she hits him over the head with a rolling pin, to get him to stop scaring the "baby". When Bugs saw that, he said to himself "Hey! this promises to be fun! Eh, so I'll be a monkey". From that point on Bugs decides to make Elvis life miserable. As Elvis rocks Bugs cradle rather unpleasantly, he tries to sneak away from Bugs who responds with a horrid tantrum "Waah, I wanna drinka water! Waah, I wanna drinka water!"; to which Elvis responds by dumping a bucket of water over him then the scene changes to Elvis still holding the bucket then fades just before the mother gorilla hits him. The scene changes and they're outdoors, where MAMA tells Elvis to "play horsey with baby". Elvis plays for a few seconds then sends Bugs flying up into the air, then lands on Elvis; to which he responds by chasing Bugs. To Bugs best of luck, MAMA is nearby who soon takes control of the situation by clobbering Elvis with the rolling pin, then Bugs does the same while saying "bad ol' daddy" (almost like Tweety's famous line, "Bad ol' putty tat".)
MAMA leaves Bugs in the care of Elvis once more, this time with Bugs hitting Elvis constantly over the head with a baseball bat. MAMA walks away while saying "yeah that's it, keep baby happy". Elvis then takes the bat and breaks it in two, but Bugs yells "MAMA", and Elvis decides to replace the bat for Bugs; rather that letting MAMA know what just happened. While this is happening the stork is already taking to MAMA about his mistake, then gives her their real baby, Elvis hears MAMA yelling: "Elvis look! The Stork brought us our real baby". Bugs finally appreciates the danger he is in, and tried to run away. Then he crosses a rope bridge and tries to keep Elvis at bay threatening to cut it if he crosses it; Elvis instead pulls the entire opposing cliff-side to him in one effortless yank of the rope. He tries to hit Bugs, but he got away to the bottom of the cliff. When Elvis sees him, he throws a huge boulder toward Bugs. Bugs has no idea that there's a boulder coming towards him, but moves away when he sees MAMA coming to say: "ELVIS! Guess what the baby said?" while she steps right into the spot where the boulder should land! Elvis realizes the misfortune of what just happened, and tries to apologize to MAMA, but she begins to hit him with the rolling pin off-screen. Bugs says: "I'd like to see him eeh-ooh-aah-ooh and but his way outta this one", while the stork mistakenly delivers a baby to Bugs. The baby turns out to be Daffy. Daffy closes the cartoon by kissing and hugging Bugs and saying: "Ooh, I love you mommy!".