1809, American English, from dough + nut (n.), probably on the notion of being a small round lump (the holes came later; they are first mentioned c. 1861). First recorded by Washington Irving, who described them as "balls of sweetened dough, fried in hog's fat, and called doughnuts, or olykoeks." Earlier name for it was dough-boy (1680s). Bartlett (1848) meanwhile lists doughnuts and crullers among the types of olycokes, a word he derives from Dutch olikoek, literally "oil-cake," to indicate a cake fried in lard.
The ladies of Augusta, Maine, set in operation and carried out a novel idea, namely, the distribution of over fifty bushels of doughnuts to the Third volunteer regiment of that State. A procession of ladies, headed by music, passed between double lines of troops, who presented arms, and were afterwards drawn up in hollow square to receive from tender and gracious hands the welcome doughnation. [Frazar Kirkland, "Anecdotes of the Rebellion," 1866]
Meaning "a driving in tight circles" is U.S. slang, 1981. Compare also donut.