"Git along" is just a Western accent laid on to the expression "Get along!", an imperative to cattle, especially the hare-brained young ones called "dogies". The American Heritage ponders thus:

In the language of the American West, a motherless calf is known as a dogie. In Western Words Ramon F. Adams gives one possible etymology for dogie, whose origin is unknown. During the 1880's, when a series of harsh winters left large numbers of orphaned calves, the little calves, weaned too early, were unable to digest coarse range grass, and their swollen bellies "very much resembled a batch of sourdough carried in a sack." Such a calf was referred to as dough-guts. The term, altered to dogie according to Adams, "has been used ever since throughout cattleland to refer to a pot-gutted orphan calf." Another possibility is that dogie is an alteration of Spanish dogal, "lariat."

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