Pab1: You are going to be shooting a 1/4 oz. of lead out of that .56 smoothie, and at 1300 fps, it is plenty to kill deer, provided you understand that accuracy drops off rather quickly after 50-60 yards, depending on the load, sights, and barrel length. After all, you would not hesitate to use a .45 Colt Revolver to kill a deer inside 50 yards, and you put a lot less powder and get less velocity out of that revolver round than what you are expecting here.
The gun should primarily be used for small game, however. A 28 gauge shotgun is .550 in bore diameter. Sound familiar? What ever you can use a BP 28 gauge shotgun to kill you can use your new barrel to kill. Just remember that you are shooting a cylinder bore shotgun, with BP ballistics. That means its a 30 yard gun at most with most shot loads. Read V.M. Starr's article in Bob Spenser's website, " Black Powder Notebook", for loading data, and don't try to push it. For better patterns with these guns, less powder usually gives better patterns. Go to heavier shot to provide the extra pellet energy to kill small game cleanly.
Have fun.