In 1850s America, most people relied on privies and outhouses for their bathroom needs. But the Davis family of Natchez, Miss., had something few other Americans did: indoor hot-and-cold running water and an indoor toilet.

Now this marvel of 19th-century technology is getting a new home, moving from the Dunleith Historical Inn to another mansion nearby operated by the National Park Service. The new lodging will give the public a chance to see a pre-Civil War version of a luxurious lavatory, complete with shower/bath combo....