Side note: I don't think that's supposed to be Elmer Fudd. The cartoon All This and Rabbit Stew featuring that character was released in September 1941, after Elmer Fudd made his official debut in 1940 in Elmer's Candid Camera.
A Fudd-like character called Egghead had been introduced by Tex Avery as early as 1937, voiced by Danny Webb and later Arthur Q. Bryan. Many historians believe it was this character that evolved into Elmer Fudd, as both Egghead and Fudd were voiced by Bryan.
http://en.wikipedia.org/wiki/File:Daffy_Duck_and_Egghead.JPG
http://en.wikipedia.org/wiki/File:ElmersCamera.jpg
They redrew the black hunter into the Elmer Fudd we know today because of the racial implications.
http://aaea-la.blogspot.com/2007/09/bugs-bunny-was-originally-black.html