Prairie dogs are squirrel sized. The killing is no big deal, as far as what bullet is used from a .223.
The only real issue is the accuracy of the load.
People worry too much, get too nit-picky, about what bullet, what cartridge, etc., etc., on stuff like prairie dogs.
A .17 Mach II is plenty good to 100 yards. Once the wind and drop are determined by the shooter, they're adequate to 200 yards. That's what I watched, anyway.
I was getting hits to 300 yards with my .223; about six inches of holdover, roughly. On that particular day, about four inches allowance for the breeze.
IOW, go have fun.