Working Dog Commemorative Coin Act This bill directs the Department of the Treasury to mint and issue 50,000 $5 gold coins, 500,000 $1 silver coins, and 750,000 half-dollar clad coins in commemoration of the service that working dogs provide to society. The designs of the coins minted under this bill shall be emblematic of the contributions of working dogs to society, including in detection, military service, therapy and assistance. Treasury may issue coins only during the one-year period beginning on January 1, 2023. All sales of coins shall include a surcharge, which shall be paid to America's VetDogs for general expenses associated with the fulfillment of its mission.