The University of Pittsburgh, Center for American Music site: Susanna has the words, dated 1848 (same as those given by Masato, above, Songs of the Sable Harmonists). In the index it is listed as "Oh! Susanna," but at the head of the lyrics, it is simply "Susanna."
The verse about New Orleans may have been added later, but in the same year (for a trip to New Orleans by the Christy Minstrels?). (The Christy Minstrel sheets do not mention Foster as composer).

The Christy edition (Holt) 1848, also posted by Masato, has several Foster songs. The song was also printed singly, as shown by the Levy site, where the 1848 cover is preserved. It would be interesting to see the words accompanying this cover. Is the New Orleans verse there?

The sheet music of the version "written by Wells", 1850(?), pub. by Benteen in Baltimore, has the New Orleans verse. Oh! Susanna
More than one rewrite by various lyricists came out in 1848-1849, illustrating the popularity of the song.