I visited the Hermitage in 1995 and remember the slave cabin, but it looked like a modern reconstruction, not an original building from the time that Andrew Jackson lived there.
Aside from the actual logs (eastern red cedar) I seriously doubt that the rest of the building is authentic to 1840. For incidence, I doubt that a slave cabin in Tennessee would have had a wood floor. Most of the cabins I've seen around here that still exist have dirt floors.