"shoot with a gun," 1620s, from gun (n.). Related: Gunned; gunning. The sense of "accelerate an engine" is from 1930, from earlier phrase give (her) the gun (1917), which appears to have originated in pilots' jargon in World War I; perhaps from the old military expression give a gun "order a gun to be fired" (c. 1600).
modification of Old English huntung "a hunt, chase; what is hunted, game," verbal noun from hunt (v.). Bartlett (1848) notes it as the word commonly used by sportsmen in the Southern states of the U.S. where in the North they use gunning. Happy hunting-grounds "Native American afterlife paradise" is from "Last of the Mohicans" (1826); hunting-ground in a Native American context is from 1777.