Dogman appears in Cat-Astrophe. He is Catman's old archenemy. He attempted to defeat Catman but he failed to do so. He resides at "It's a Wrap!" Retirement Community, just like Catman. His lone appearance was in the episode Cat-Astrophe. Catman thought Sparky was Dogman, so Timmy convinced the real Dogman to get out and fight Catman.
Catman and Dogman being arch-enemies might be a reference of the stereotype of cats and dogs being arch-enemies.