Hmmmm, 1000 yard white tail?
I suggest that cartridge would be a more important consideration than caliber.
The shot can be made with calibers from 6mm on up. The deciding factor is delivering a particular caliber bullet with enough terminal performance to provide a clean kill. A clean kill, to me, means placing a well designed, terminally performing bullet in the kill zone, every time.
eddybo's words are quite correct.
The shot "can" be made quite easily, but not the very first time attempted. I recall the my first attempt at 1k. The target was an 8 1/2 X 11 piece of paper mounted vertically. After tons of $ (at least to me), load tuning, drop chart development out to 800 yds +, the target was finally placed at 1105 yards. As close to the magic 1k as I could get.
It took a long time to get my guts up to make the shot. In my mind that paper was pasted over the kill zone of a world record bull elk. Checking clicks and drop chart was checked and rechecked. Wind was read, studied, reread to the point of anxiety. The trigger broke. The shot was spotted. Snow flew behind the target holder. At least I hit the target holder, that wasn't all that large. With renewed confidence I held the same as the first shot and let'r rip. Snow again flew close to the same spot behind the target.
The long walked revealed two shots within 3" of each other and IF the pages would have been turned horizontal I'd hit the dang thing at least once.
Yep it's easily made all right if it weren't for the durn wind.
Envision that buck hanging on your wall and go for it.gun)