I shoot a 357 1894C myself. Same style rifle, just less punch.
Your rifle will serve you just fine on deer, and even bear as long as you keep your ranges within reason. I regularly kill deer with my 357, and have killed them cleanly slightly past 100 yards. I know if the 357 works that well, your 44 magnum will with ease.
I think you'll love that gun after you play around with it some!