This is a very interesting - and fun - question.
The expression פה קָבוּר הכלב might be older, but I know it from a 1973 song from the album "Sippurei Poogy" by the band Kaveret. The writer, Danny Sanderson, is known for using many puns in his songs.
The song lyrics are:
פה קבור הכלב - Po Kavur HaKelev (Here is where the dog is buried - ここに犬が埋葬されて)
פה קבור הכלב - Po Kavur HaKelev (Here is where the dog is buried - ここに犬が埋葬されて)
זהו עצם העניין - Zehu etzem ha'inyan (That is the point - それがポイントです)
לא, זה העצם של הכלב - Lo, ze etzem shel ha-kelev (No, that's the dog's bone - いいえ、犬の骨です)
אבל הכלב מת מזמן - Aval ha-kelev met mizman (But the dog died long ago - でも昔犬死にました)
טוב, זה עצם העניין - Tov, ze etzem ha-inyan (Yes, that's the point - はい、それがポイントです)
There are several levels of pun in these words. First, the word עצם (etzem) has multiple meanings ("bone" as well as "essense" or "core issue" - 中心的な問題)
But the main pun is from a very old the German expression: "Da liegt der Hund begraben" (this is where the dog is buried). The meaning of the expression (in German and Yiddish, and then translated to Hebrew) is "this is the basis of the issue," "this is the core problem" or "this is the crux of the matter" (問題の核心).
I've read that originally, instead of "hund" (dog) - this expression was used the word "hunde" or "hinte" (buried treasure, or treasure chest).