"Braes o' Balquhither" - the lyrics in the Bodleian are not related (Let us go, lassie, go) to "The Orphan Girl" nor are the similar versions in the DT.
Midis for two versions of "Braes..." are in the DT, but are much too lilting to be suitable for the words of "The Orphan Girl."

The "Orphan Girl" posted by Masato from the Sacred Harp (1905) is the same as one of the Randolph versions posted earlier.
Variation among the versions is small, suggesting that the original was a printed source. So far, the one Masato provides from the Sacred Harp could be the source of most of the versions in the folk song collections and on record. Evidence for an older version is anecdotal ("1885," etc.) although the subject matter is Victorian in feel and matches the pathos of other orphan songs and stories of that time.

Randolph and others provide sheet music which would be interesting to compare with that of the Sacred Harp.