I'm surprised no one has mentioned this is derived from the Irish song, "Old Man Rocking the Cradle":
Hi ho, hi ho, my laddie lie aisy
For perhaps your own daddy might never be known
I'm sitting and sighing and rocking the cradle
And nursin' the baby that's none of my own

The song of an orphan child becomes a song of an orphan calf.

Owen Wister gives us a valuable place in time for the cowboy
rendition in 1893 but there is an earlier mention.
Andy Adams in his "Log of a Cowboy" speaks of it while driving
a herd across the Platte in 1882.

'...Within a short time, some one in the lead wig-wagged his lantern; it was answered by the light in the rear, and the next minute the old rear song,--

    "Ip-e-la-ago, go 'long little doggie,
    You 'll make a beef-steer by-and-by,"--

reached us riders in the swing, and we knew the rear guard of cattle
was being pushed forward...'

So now you've got a story for this song.

Rex