Meant to copy you on my reply to invisible hand. In that video, the guitar is a Wayne Henderson (VA) custom cutaway acoustic. On most other videos, except early black and whites, you’ll see Doc playing a Gallagher (made in Wartrace, TN.
Doc referred to a Les Paul when he talked about developing his flatpicking of fiddle tunes. He played them in a country band, on electric guitar—a Gibson Les Paul model, which is a solid body legendary design by the great, deceased genius Les Paul (he of the Les Paul/Mary Ford duo, inventor of multitrack recording and the loop tape special effect).