I guess I will throw in my two cents worth here. I hunt "dogs" all through the spring, summer and fall. Two of my friend and I try to do a week a month when the dogs are up – we are ROF's (retired old farts). Shoot I even carry a couple 'dog' guns to deer camp (hunt the same area). I usually carry five rifles and two pistols: 17 Mach IV, 17 Remington, 223 Remington and 22-250 Remington along with a 17 HMR and two 14" Contenders one in 223 Remington, one in 221 Fireball. I limit my 17 calibers to about 250 yards. But the two 22 caliber rifles I have no problem going out to 500 yards. I have also carried a 6mm Remington and 6.5 Grendel for fun. One thing I do use exclusively is a fragmentable type of bullet (Hornady V-Max and SPSX, Nosler Ballistic Tip Varmint and Varmageddon). Where I shoot, north-central Nebraska, south-central South Dakota and east-central Wyoming, is relativity flat. In the past there have been problems with 'city slickers' shooting cheap FMJ bullets and slinging that slug all over the place. The FMJ bullets have a big problem with ricocheting while the fragmentable type disintegrate upon impact (be it a dog or dirt).
As for the amount of ammo, well that depends on how hot the shooting is. I have completely run out on occasion.
You can use anything to shoot a 'dog", I even shot one with a Sharps 40-65 WCF once. But remember, if you start slinging bullets all over, you might not be asked back!
Just my own personal opinion.