Elmer's Pet Rabbit is a 1941 Merrie Melodies cartoon directed by Chuck Jones. It is the first cartoon in which Bugs is given his name (on a title card).
The music in the cartoon includes a variation on "While Strolling Through the Park One Day" (Ed Haley), arranged by Carl Stalling, performed by Elmer and Bugs. Elmer, of course, has trouble with many of the words, due to his "rounded L and R" speech impediment.
Elmer buys Bugs Bunny in a pet shop and Bugs Bunny begins by questing his lifestyle that Elmer provided for Bugs since he is a rabbit. But what comes next becomes really looney when Bugs moves in with Elmer and causes havoc.
Bugs Bunny wears yellow gloves, he has a deep voice, and he has no buck teeth (unless on "Featuring BUGS BUNNY" screen). Though this cartoon was released after A Wild Hare in which Bugs' recognizable "Bronx/Brooklyn" voice characterization appears for the first time, Mel Blanc used the voice from Elmer's Candid Camera in this short.
This was the second cartoon for Bugs and the 23rd cartoon that Chuck Jones directed.
In this cartoon, Bugs personality is radically different from his other incarnations; as opposed to his usual fun-loving and comic relief personality, he has a much more aggressive, arrogant, disrespectful, almost thuggish personality. Also, he is more sarcastic than wisecracking.
This is the only cartoon where Bugs claims to not eat carrots (although he eats them and other vegetables while complaining).