Just as a FYI, Hunter Arms offered a "The Trap Gun" buttplate which is commonly found on c. 1890-1910 00 to No. 2 grade guns.
Not sure what the dog and duck had to do with Live Bird and Inanimate Targets
No "Trap Gun" was advertised in the pre-1913 catalogs, but their Pigeon Grade "The only American Pigeon Gun made" was introduced in 1893.