giddy-up interj.

command to a horse to go, 1909, probably an extended form of earlier giddap (1867), itself probably from get up. Compare gee.

The terms used to start horses in harness and to urge them to a better appreciation of the value of time comprise vulgar corruptions of ordinary speech and peculiar inarticulate sounds. Throughout England and the United States drivers start their horses by picking up the reins, drawing them gently against the animals' mouths, and exclaiming go 'long and get up; the latter appears in the forms get ap (a as in hat), giddap, and gee-hup or gee-up. [H. Carrington Bolton, "Talking to Domestic Animals," in The American Anthropologist, March 1897]