I don't hunt anymore but I believe that my load generates about 1000 fps & I would not hesitate to hunt deer sized game with it out to 100 yards. I have read that (some) lead bullets should not be loaded above 1000 fps to avoid barrel leading problems. I don't know if that is true because like I said earlier my load is not that fast.
The leading issue is real enough. But, whether a bullet may be used at a given velocity depends on it's alloy composition. At the regular old-time handgun velocities for cartridges (.45 Colt, .44 Special, .44-40, .38-40, .38 Special, .455 Webley, .45 ACP, etc.) just about any alloy will work, no matter how soft the bullet is. At 850 FPS for example, recycled .22 LR range scrap bullets work great.
Also, .44-40 cartridges were loaded with fairly soft plain lead bullets, well into the 20th Century, reaching 1250 FPS in rifles.
Lyman (Ideal) #2 lead alloy is mentioned as the standard for cast lead bullets at such velocities. Not hard cast and not soft cast either, and capable of mushrooming in deer-sized game. Really, it's at higher velocities when leading becomes an issue. And then, if need be, you can add some tin and antimony into the mix from salvaged linotype, 50/50 bar solder, etc. using formulas in the Lyman Cast Bullet Handbook or found on-line. And, of course, a good bullet lube and a cast bullet with generous grease grooves is essential.
Your 1000 FPS load is close to the original .44 Henry rim fire loading used in the 1860 Henry rifle and 1866 Winchester rifle, which I'm sure killed many a deer for the pot. Arguably a contender for the gun that won the west, alongside the 1873 Winchester. The Henry load is listed at 1125 FPS with a 200 grain lead bullet, which is a bit faster. But, I'm sure that you could increase your powder charge a bit and use your same bullets with no problems if you wanted. Personally, I think that 100 yards is a bit too far. 70 Yards might be a wiser maximum range with such a load, but if you can put it into the heart/lung area, that's what counts.