Jokes suggesting dog urination seem be littered all over Tex Avery cartoons (Dog! Litter! Get it?). I don’t know how many of his cartoons included a dog/tree gag. His variation was a dog/fire hydrant gag. He uses it in the first Droopy cartoon and he fits it into his panic-paced stream of gags in The Cat That Hated People when the title character rockets to the moon.
The cat’s continually roughed up by objects that have a connection (such as a hammer and a nail). After one abuse gag, he looks off camera and sees the next gag coming. The second and third drawings below are consecutive. Avery didn’t waste time in this cartoon.
Avery maintains the take, but not by exaggerating the drawing. He simply slides it around on the background to indicate fright.
The cat jumps out of the scene and the gag runs into view.
Heck Allen wrote the story. Bill Shull and Louie Schmitt joined Walt Clinton and Grant Simmons to animate it.