According to Saunders and Root's The Music of Stephen Foster, vol. 1 (pp. 477 and 496), this (from the Levy collection) is "The earliest known copy." Saunders and Root note: "Foster probably did not prepare this arrangement. His name does not appear anywhere on the songsheet....":

Title: [Foster-Hall Reproductions]. The Celebrated Ethiopian Song. Camptown Races. Arranged for the Guitar.
Composer, Lyricist, Arranger: [Stephen C. Foster].
Publication: Baltimore: F.D. Benteen, 1852.
Form of Composition: strophic with chorus
Instrumentation: piano and voice
First Line: De Camptown ladies sing dis song, Doo-dah! doo-dah!
First Line of Chorus: Gwine to run all night! Gwine to run all day!

~Masato