The first revolver was patented and sold to the military in 1820, the Artemus Wheeler.
Here's a link to a webpage with pictures of this revolver as well as the basic information about it. Link
It's a neat gun and as far as I could tell the first "real" revolver to be used during the 19th century. Other guns were developed during the 19th century and admittedly this one wasn't all that common. Since it was used by the military, my character had to have some background or connection with the Navy. Be realistic with the weapons you choose. I found this to be a terrifying weapon to look down the barrel of, so I used it.