I’ve only killed one deer with 45 Colt. I have three m25-5 S&Ws. Two are set up for target loads and one set up for 250Gr traditional RNFP. I picked up wrong case and had WC pistol & Ammo. The 242gr button nose WC at 700fps, cast very soft. I shoot iron sights so I limit shots to 50yds, this one was about 30yds. It flopped around and naturally ended up 50yds down hill, but it were dead.
I have killed one deer with a 1911 Gold Cup and several with 44mg. There is no reason a 1873 in 45 Colt won’t take deer at 100yds. I only shoot 50yds with handgun because of self imposed limit.
Out of rifle 100yds is no big deal. I’ve shot many deer in eastern states. I have never shot a deer with pistol cartridge carbine or rifle. The bulk of deer shot with rifle were 35Rem/ Rem 141. Most shot on the run under 100yds. Second place 30/30. Deer ain’t Cape buffalo, your 1873 will do fine.