I think Genie is the one who gave dates of 1849 and 1859 for Higley's poem; they appear nowhere else but in her posts. Of course they are incorrect as Artful Codger points out; Dr. Higley came to Smith County in 1871.
"Western Home," with Dr. Higley's name attached appeared in the Kirwin [KS] Chief, Feb. 26, 1876 (The page is photographically reproduced in White, John I., "Git Along, Little Dogies," p. 162; Univ. Illinois Press). It is supposed to have first appeared in the 1873 Smith County Pioneer, but no copy has been located.
All this was posted in thread 6501: Origin Home On the Range
The music also appeared before the printing by Lomax, used in Goodwin's sheet music for "An Arizona Home," 1905. Research by Samuel Moenfeldt, a lawyer for Schirmer, the music publishers, obtained affidavits from many westerners that they knew the song before the Goodwins published it.
An 1885 letter written by Bob Swartz of PA, who had tried mining in Colorado, contains the lyrics to a song he claimed was his, "Colorado Home," which has words almost identical to those of the Goodwins.
The music seems to be much older than 1905, the date of the Goodwins song; Mr. Moenfeldt recorded "Western Home" as sung by Blind Clarence Harlan, who said he learned the song in 1874. White set down the music in his book, p. 163; in 3/4 time, he says it is "close enough to the well-known melody of today as to be recognizable."

Lomax claimed to have obtained the music from a Negro bartender in San Antonio, Texas; but it probably dates to Dan Kelley and the Harlan Brothers ("The Harlan Orchestra") who set Dr. Higley's poem to music in the 1873-1876 period.

These and other details in John I. White's book.