The imagery of this phrase is vivid. I agree with Azizi that its use of "squat" as a transitive verb is parallel to "squash." This use of "squat" could be influenced by both "squash" and "swat." (I'm not sure of the etymology of "squash" but "quash" is a synonym for that verb.)

On seeing a foolish rabbit coming up in the same place repeatedly, you would soon anticipate it and bag the prey with missile or trap. (Well, maybe not now, but a generation or two ago...) If you notice a familiar idea popping up again and again in the same old way, eventually you'll get bored enough to throw something at it, knock it down, or otherwise quash that remark or "squat that rabbit." The silly thing's been hopping around enough already. Stomp on it, somebody, please.

Maybe that's not the original meaning, but it's the image the phrase evokes for me. The anatomical connotation could be an overlay, putting innuendo into a normally innocuous metaphor to add interest to the song.

Trying to read "squat" as "force [the rabbit] into a squatting position" just doesn't work for me. I can't imagine ordinary people who would bother, or wish, to do this. I usually find that folklore imagery evokes some sort of familiar or plausible metaphor (with or without fantasy elements).