The Duke University site (you can find it through the links) includes a copy of Finnegan's published in the US in 1838 (click here). The data synopsis with it would lead you to believe that was the original, but when you actually view the work, it is clearly titled as "an arrangement of the popular Irish song". I don't know any earlier publication dates, but the song evidently pre-dates 1838. I think you can safely consider the song traditional by most definitions.