Targets for 1000 yard matches are pretty big. Would it even be possible to clean kill a prairie dog sized target? Probably will need a .30 caliber rifle, which would be pricey to shoot. Better to sneak up a bit and use a .223 or .22-250. Even a 1 MOA rifle, plus wind and mirage would struggle to hit a prairie dog consistently if at all at 1000 yards. Yeah, there is probably a U-tube video with a person doing it.
The course of fire on the range I shot at 1000 yards was 4 targets: 16" Square (1.5 MOA), 10" Round (1 MOA), 8" Square (3/4 MOA) and 5" Round (1/2 MOA). My Savage Model 12 223 (1:9 Twist, heavy stainless, Target Single Shot, Left eject, right hand bolt) will shoot 3" at 1000 yards. I believe they discontinued this rifle a few years ago. But 3 friends have this gun in 6BR 1:8 twist, and one has a 22-250 1:9 twist. They are still out there! I bought mine 6 years ago used 6 years ago with scope, bases, rings, 2000 bullets (same lot #), 16 pounds of powder (same Lot #) 2000 Rem 7 1/2 Primers (same Lot #), 500 Brass (from LC over run a few years back!), dies and loading data. All for $1900, about fair market value at the time!
Pop can size targets are very doable with good quality rifles straight out of the box. Savage makes them, Ruger makes them, Remington say they do, but not without some work, that I've seen!
The cartridge choice is problematic if you want 308, but .223 Rem, 6 BR, 6 & 6.5x47, 6 & 6.5 Creedmoor, and 6.5x284 are all doing it, but not with store bought ammo Remington, Winchester, and Hornady ammo (the Lapua Brand factory 6 BR ammo has been astounding!, .25 MOA and Better at 1000 yards!)
Ivan