Hmm, I replied about 5 hours ago but it never showed up...
Anyway, no I am not implying that a .62 will not penetrate a deer. The point I am trying to get across is that you will be severely limited in taking a deer quickly and humanly when using such a short barrel. Even a large caliber round ball needs a decent amount of velocity to penetrate sufficiently to cause the animal to bleed out quickly and with a 12 inch barrel you will be hard pressed to do that. I'm not going to say that the bullet needs to generate X amount of energy at ____ number of yards or repeat any of that internet nonsense, I am going to say that even stuffed with a maximum safe charge of powder, the effective range of your pistol is still going to be extremely limited. Add to that is your sight radius which won't even be the full 12 inches of the barrel plus a number of other variables makes for a terrible plan in my opinion. Yes, I know that modern pistol hunters using things like the T/C have shorter barrels and hunters regularly take deer at more than 50 yards with them but that is the big difference between smokeless and traditional black powder as far as either's ability to push a bullet to a sufficient velocity with which to put the animal down quickly.
As a responsible hunter you owe it to your game animal the quickest, most humane death possible. Using your pistol loaded with shot (which I assume is a smooth bore) for small game at limited range is I think, fine, safety concerns aside. Loaded with RB on a deer is ill advised and has a very real chance to be unnecessarily cruel.
Lastly, a razor sharp broad-head even at relatively slow speeds does a lot of damage quickly because the frontal surface area (the razor's edge & what impacts the flesh and/or bone) is minuscule compared to a round ball. To compare the two is an unnecessary tangent and not related to your original question. You admit that you do not have experience with black powder pistols and asked for guidance so that's what's been given.
Please don't take a chance on wounding a deer by using your smoothbore pistol even if it is legal in your area.