Actually, "Turkey in the Straw" is more likely derivative of "Natchez Under the Hill," bit the two are so similar that they're essentially variations of the same tune - "Old Zip Coon" (1833). It has been claimed that the progenitor was the English "Rose Tree in Full Bearing," but I hear no real resemblance.

"OZC" is usually attributed to G. W. Dixon (1834), but a newspaper clipping of 1833 associates with Bob Farrell, another blackface performer. "Natchez Under the Hill" appeared in 1839.

The title "Turkey in the Straw" looks like a latecomer. I haven't found it in print before 1893, though the reference is to around 1870.