223 is great for short to medium range dogging. once you start stretching the range, there are some things that would be easier accomplished by a cartridge w/ a little more whoop-@** to it. however, the expense is recoil.
great long range doggin' cartridges would include 243, 25-06, 308. the hotter magnums are, of course, great, but when you are talking 200-500 shots in a day...
i prefer long-range dogging, and i'll actually refuse close shots. i believe dogging is a great way to push the envelope. i already know that anything inside of 300 yards is a gimme, therefore, i look for shots beyond 300 yards. doing this keeps my skills sharp, keeps the round-count down to under 200, and teaches me tons about ballistics and wind doping.
anyway, to answer your question...at long range (around 800 yards), a 223 might knock a prairie dog over, but probably won't punch a hole in him. at ranges around 375-400 yards, a 223 ceases to have explosive effect on prairie dogs. in anything more than a gentle breeze, you really need to be good at wind doping.