No you don't need a beagle to hunt rabbits, although it can greatly increase your chances of being successful. Especially when hunting alone if you don't shoot the rabbit when you jump it, you most likely won't get another chance. The dogs can give you several chances if needed. The thickest of briars and treetops, but not so much in deep woods,more near fields, plus tall grass fields "crep fields" are really productive. Anyshotgun other than 10 gauge, or a 22 will work if aimed correctly. It'll be hard to hit one running with a 22 though. I shoot most rabbits that circle after they stop hopping, but always use a 20 gauge for them running or shooting through the brush shots that would be difficult with a 22.