The story
Of American origin. First use appears c.1856. Popularized by appearing in a sermon parody attributed to William P. Brannan as "Where the lion roareth and the whangdoodle mourneth for her first-born," published in The Harp of a Thousand Strings: Or, Laughter for a Lifetime (1858). Roald Dahl uses the term in at least three stories of his: James and the Giant Peach, Charlie and the Chocolate Factory, and The Minpins. In at least two of those stories, namely Charlie and the Chocolate Factory and The Minpins, the whangdoodle is stated to be a vicious monster.
Etymology from Wiktionary, CC BY-SA 4.0.