I seem to remember seeing Roger Rabbit in some cartoon shorts before the movie "Who Framed Roger Rabbit" came out, but I can't seem to find out where I saw them. Was Roger Rabbit an established cartoon character prior to that film and were there any other Roger Rabbit shorts that exist outside of the film?
Roger Rabbit originated not as an animated character, but rather as a literary character in the 1981 book "Who Censored Roger Rabbit", where he played a sidekick to Baby Huey. This book was later adapted to the film "Who Framed Roger Rabbit", released in June of 1988.
However, Roger makes at least one appearance as an animated character before the release of the 1988 film. He made a cameo in Sport Goofy in Soccermania, which came out in 1987. This was the only pre-film appearance I could find.
He also makes several appearances that postdate it, notably in November 1988, where he appears in "Mickey's 60th Birthday", where he mistakenly uses a stick of dynamite for a candle and blows up the set.
There are also a couple of appearances ("New Character Day" and "Buster and Babs Go Hawaiian") in Tiny Toons Adventures that also postdate the film release.
The character comes from Who Censored Roger Rabbit? by Gary K. Wolf published in 1981. While the characters are from the book, the scenario is very different. The characters are comic strip characters, who speak in word balloons, which decay away. A key plot point is a word balloon that hasn't decayed and is still around for Eddie Valiant to see. Characters such as Baby Huey and Jessica Rabbit are in the story, for instance.