This episode possibly takes place sometime around Halloween, as evident from the jack-o'-lanterns around the place, and the dance being called the Four-Legged Fall Ball.
The elephant, Jimbo, is a possible homage to the character Dumbo, with the train serving as Casey Junior.
Roger tries to get "My Little Aquarium Pals", a possible homage to the "My Little Pony" line.
According to the deed of the Dearly Farm, outside of animals already on the farm, the Dearlys are only allowed to have 101 pets.
The scene with Jimbo on the Chow Tower is a likely tribute to the well-known scene from the King Kong films.