Not 19th century; late 17th to early 18th century button made to commemorate the marriage of Charles II and Catherine of Braganza in 1662. Your site being mid to late 18th century doesn't necessarily mean that the button isn't that old, just that it was worn and lost decades after it was manufactured. I've found 17th century shoe buckles and coins on 1760-1770 sites. I also routinely find cone shank tombacs on Civil War era homesteads. Serviceable buttons or all ages may have been dug out of button jars to replace a missing one in a pinch.
It's pewter so make sure to seal it to prevent it from crumbling, but that's a seriously cool find. Congrats!