Not the right thread for this, but here goes:

Owen Wister, author of "The Virginian," collected "Git Along Little Dogies" about 1893 in Texas (his notebook for February-March, 1893). The chorus was:
"Sing hooplio get along little dogies
For Wyoming shall be your new home.
Its hooping and yelling and cursing those dogies
To our misfortune but none of your own."

Wister provides five verses and chorus.
Wister was a trained musician, so he took down the air as well as the words. From "Git Along Little Dogies," 1975, by John I. White, pp. 16 ff.: "Apparently this also remained hidden in his desk until 1932, when he presented the music to John Lomax, who incorporated it into ABFS, 1934."

[In 1960, Lomax and Lomax in "The Folk Songs of North America" threw out all the Wister words and music and tell a different story- and put in a version from the singing of a Frank Sullivan, "who learned it from cowboys in Idaho in 1910." This one throws in a "cradle" verse that has nothing to do with the rest of the song, and ignores the Wister material altogether. In my opinion, the Lomaxes cut the new story from the whole cloth.]

White says that "In recent years, several authorities on the subject have stated that the unknown composer of "Whoopie Ti Yi Yo" modeled his song on an old Irish ballad that began 'As I was a-walking one morning.'"
To illustrate, White included these words in his write-up, from Oscar Brand.
As I was a-walking one morning for pleasure,
Down by the still waters I joggled along,
I met an old man making sad lamentation,
And nursing a baby that's none of his own.
Ee-ay-oh, my laddie, lie easy,
It's my misfortune and none of your own.
Ee-ay-oh, my laddie, lie easy,
It's my misforture and none of your own,
That she leaves me here weeping and rocking the cradle,
Minding a baby that's none of my own.

Words from Oscar Brand, "The Ballad Mongers," 1962, Funk & Wagnals, NY. Where was Brand's version from? Was it cobbled together?
Lomax, FSNA, 1934, printed another version, "The Old Man's Lament," three verses and chorus, "collected and arranged by Seamus Ennis."
Although collected in Ireland, the song could just as well have been English in origin, since broadsides flooded both ways.
Is "Git Along..." descended from "lament, cradle song"? Possible, but not certain.

Where were the cowboys from? Hard to tell. The typical outfit moving cattle on the trails was a mixed bunch from the entire eastern half of the US, the British Isles and some from Canada and Mexico. Perhaps even the odd Aussie; some came for the California gold and ended up in cattle (some still come and get work on the operations in western Canada).