also heehaw, first recorded 1815 (as Hiu Haw), probably imitative of sound of donkey's bray (cf. French hinham). As "a loud laugh" from 1843.
Examples from the Web for hee-haw
But on a sudden we did hear a noise—a rattling and "Hee-haw!"Pluck on the Long Trail|Edwin L. Sabin
At last the poor donkey could stand no more and, lifting his head, he uttered a loud “Hee-haw!”Beasts & Men|Jean de Bosschre
From the woods at his left came the protesting "hee-haw" of a mule.Tom Swift and his Motor-cycle|Victor Appleton
Hee-haw never runs far, an' he never did such a thing before.The Moving Picture Girls at Oak Farm|Laura Lee Hope
"Do hee-haw in the House of Commons, Heavyside," says the young man with a languid air.The Newcomes|William Makepeace Thackeray