I’ve been hunting prairie dogs since 1975 and don’t seem to have visibly reduced their numbers, but I have learned a few things along the way. I’ve shot them with probably a dozen cartridges from the .17 Mach IV to the .338, and I think that without question, the best dog load is the .223. It doesn’t have the range of the .22/250, and won’t produce as many Olga Korbuts and Mary Lou Rettons, but its small powder charge allows you to shoot and shoot and shoot without your barrel getting so hot that you have to stop. Also, before the Great Obama Panic, .223 ammo was cheap, and someday may be again. By the way, the .338 bucks the wind very well, but it spoils too much meat.
The best scope for dog hunting is a variable that goes from around 6X to 20X, or higher. Twenty-four power or 30 power is even better. Also, it must have a mil dot reticle. A dog scope without mil dots is as worthless as a condom with holes. You have to do so much allowing for wind and distance that you’re lost without them. You spot dogs by cranking down the power, and when you find a likely one, you turn it up to wherever you want. Spotting with binoculars and switching to a scope will drive you nuts; you won’t be able to find where you were looking with the former when you switch to the latter. If you want to spot for another shooter, a spotting scope is better. This is the only type of hunting I can think of where binoculars are not indispensible .