As noted above, O'Reilly's poem was titled "At Fredericksburg, December 13, 1862"- I think the verses I quoted are a fragment.
The ca. 1875 date mentioned by Lighter is reasonable as this was the time that O'Reilly was a close friend of Walt Whitman's, and Whitman was writing some poetry about the Civil War.

That printing in the Pittsfield newspaper may have been the first, followed by the copy in Harper's. The latter, in the article linked by Peace, would have insured rather wide circulation of the poem.