If I could name a fault of a Beagle it would be that they don't live long enough. I guess that could be said of any breed of dog. Long ago someone said a dog is mans best friend.
Over the years I have had some great Beagles and they were all great rabbit hunters. Not only great hunters but great companions. Years ago I use to keep a rabbit dog outdoors in a pen. The last two beagles I've had I have kept the in the house. Beagles are highly intelligent and make great house pets. By keeping your dog close to you they tend to mind better.
If your looking for a beagle to hunt rabbits check their background. If the come from good hunting stock, then they will more than likely be a good hunter. My last two beagles Maggie and after She passed Dolly. Both of them were very smart and GREAT hunters
This is my current beagle, I got him when he was 6 months old and he was already started. His name is Ruger