in dancing, "a rapid whirling on one leg or on the points of the toes," 1706, from French pirouette "pirouette in dancing," originally "spinning top" (15c.), from Gallo-Roman root *pir- "peg, plug" (source of Italian piruolo "peg top") + diminutive suffix -ette. Hence, probably, U.S. Civil War slang piroot "to move or travel listlessly or aimlessly" (1863).
"to turn or whirl on one leg or on the toes," 1799 (implied in pirouetting), from pirouette (n.) and also from French pirouetter. Related: Pirouetted.