Oops, forgot to include the source for that line: Friends' Intelligencer (1854), p. 444

I should also add that, despite my above post, I've found several claims that Joseph Enoch Cornett also wrote the song. See here and here. Unfortunately, I can't find more solid evidence than either of those sites for the claim, though.

It's possible it could be a bit of mis-remembered family history. I've seen several papers where the song was quoted in reference to the death of a child named Bessie; if Mr. Cornett wrote songs (but, perhaps, not this one) then it's easy to see family members thinking he wrote the song. I should also note, though, that I haven't been able to find such an obituary online for the Cornett family.