Your .243 15" Encore will work fine of Pronghorns or Whitetail Deer. I would have to agree that you may well want or need more than a 4x Handgun Scope though.
I have used the .243 Winchester in a 15" Encore to take a couple Whitetails. That particular .243 belongs to a friend of mine. He wanted a load worked up that would work for both Whitetails and Coyotes. Since I had previous experience with the 80gr. Speer Spitzer in smaller 6mm Handguns that is the bullet I started with.
I ended up loading the 80gr. Speer Spitzers for the 15" T/C Encore .243 with H-4895 Powder. Both Hornady & Hodgdon have data available for the .243 in Handguns. The load I settled on produced 3/4" 100 yard groups from the bench at 2920 FPS.
After I had the load worked up and a supply of ammo loaded for my buddy he suggested I use it for a January Anterless Deer Season. On January 1st of that year at about sunset my chance to try it out came. Two nice sized Whitetail Does walked down the trail I was 200 yards away from. As they stopped the crosshairs of the 2x6x32mm Bushnell Elite Handgun Scope settled on the rear Doe. I held the crosshairs mid way top to bottom right behind the front shoulder. At the shot that doe dropped in her tracks, DRT.
I quickly reloaded and rested for the second Doe. She was walking at the shot and I messed up hitting her a little far back. She ran off a ways as I reloaded. I thought the range was a bit far but I was committed and settle the crosshairs right behind the front shoulder. At the shot she collapsed, DRT.
On both Whitetails there was about a quarter size exit wound, with the lungs destroyed on both. Yes my first shot on the second Doe was a bit far back (my fault) but the second shot did the deed.
I never did get to shoot a Coyote with the .243 Encore and Load, and to my knowledge neither has my buddy.
IMO I would not use bullets heavier than about 85grs. in a .243 Handgun as I am not sure they can be driven fast enough to ensure adequate expansion.
Larry
