Here's the entry from Fuld's Book of World-Famous Music (1966, 1971)

This song is apparently American, and perhaps of minstrel origin. Almost the common words, but to a different melody, appear in Row, Row Your Boat, or The Old Log Hut, copyrighted Oct. 4, 1852, by Firth, Pond & Co., 1 Franklin Square, New York, N.Y. First edition: Engraved. Front cover states that the song was sung by Master Adams of Kunkels Nightingale Opera Troupe, ascribes the music to R. Sinclair, the price is 25cents and there are two agents. m. on pp. 2—5. p.n. 1768. Back cover blank. LC(CDC— deposited Oct. 12, 1852, at the Clerk's Office, Southern District, New York, and Dec. 3, 1852, at Smithsonian Institution, Washington, D.C.) and JF. The same words to a different but unfamiliar melody were copyrighted Dec. 13, 1854, under the title Gently down the Stream by Berry & Gordon, New York, N.Y., referring to Ceo. Christy and Wood's Minstrels; LC(CDC) and JF.
The common music, and the common words, appear for the first time in The Franklin Square Song Collection, selected by J. P. McCaskey, published in New York, N.Y., in 1851. The music and words are at p. 69; E. 0. Lyte's name is given as the composer or adapter of the music and words. In the first edition of this work, deposited at LC on Aug. 27, 1881, vol. I is not mentioned on the covers or title page, and there is no reference to 1884 on the verso of the title page. Also at JF.
The song is a round or canon.