Which English phrase is often mistakenly thought to derive from rhyming slang for a Hanna-Barbera character, but actually dates back to the 19th century and is of unknown origin?

"Don't have a scoobie" is rhyming slang for "Don't have a clue". It is believed to be of Scottish origin however, is often ascribed to the Hanna-Barbera character "Scoobie Doo".

Ironically, there is a 2006 episode of the cartoon titled "Shaggy & Scooby-Doo Get a Clue!"

https://wordhistories.net/2020/02/15/not-have-scooby/
https://www.scotslanguage.com/articles/view/id/4679
https://scoobydoo.fandom.com/wiki/Shaggy_%26_Scooby-Doo_Get_a_Clue!

Sadly this is not the answer I was looking for as I think not having a Scooby is a recent phrase not dating back to the 19th century.

I will try again... this time

Barney Rubble is a Hanna Barbera product
https://flintstones.fandom.com/wiki/Barney_Rubble

Barney Rubble is often used rhyming slang for trouble, though Wiktionary appears to indicate this is incorrect
https://en.wiktionary.org/wiki/barney

Though other sources would argue to the contrary
https://www.kaplaninternational.com/blog/learning-languages/eng/top-10-must-know-cockney-rhyming-slang-phrases
and
https://www.ef.com/wwen/blog/language/11-bits-of-london-slang-you-should-know/

That said, Wiktionary does indicate that the term emanates from the 19th century and is of unknown origin. Barney, by itself, is slang for an argument or noisy dispute. This also seems to stem back to the 19th century and has an unknown origin.
https://www.etymonline.com/word/barney