A Dr. James Malachi Pelot came to Brownsville (now Sweet Springs, MO on I-70 an hour east of Kansas City)about 1870, perhaps drawn by the mineral water spring and the town's population growth due to the spring. While there were other Pelots who served the Confederacy, including other doctors, this seems the best match, as you have devined. A doctor named J. M. Pelot was a member of Kansas' first medical society incorporated 1959. It is likely the same person. As a child and young adult, I was frequently in the Brownsville/Sweet Springs home built by Dr. Pelot and have a few mementos of both Dr. Pelot and his son Will C. (born 1869). While youngest son Charles recounted some of his father's and older brother Will's interesting personal histories, I never heard that Dr. Pelot was in Kansas during that remarkable period before the Civil War.
C. S. Nold