Hey Armycar,
Welcome to the ranks of us bunny hunters. Beagles, as I'm sure you know, are smart, affectionate and dedicated hunters. It sounds like you dog has "started" himself. I wouldn't encourage him to hunt anything else but rabbits/hares. Keep him away from varmints, deer, etc...
Do like the previous poster said and get your self a beagle bell for his collar. You might want to invest in a new plastic coated "safety collar" that has a center ring that allows the collar to roll if the dog gets caught/tangled while hunting. It will prevent him from strangling accidentally. All of my beagles sport such collars in "Blaze Orange" color.
Depending on the type of cover/ground you're hunting you'll need to adapt your hunting tactics accordingly. In heavy cover, i.e., rose bushes, alders, etc... you basically need to find a relatively open shooting lane that the bunny will have to cross while running from the dog. I generally try to find the highes spot with the best field of view that I can to help to see the bunny.
As a new hunter, you need to be very careful not to shoot your dog. Bunny hunting can be very exciting and you need to learn when NOT to pull the trigger. Sometimes the beagle can be right on the bunny's tail, and if you shoot before making sure that the dog isn't in the line of fire you can end up hitting your dog. The dog can actually run into the shot pattern. If the dog is too close, pass on the shot, the bunny will be back for another pass.
Bunny hunting solo means that there is a greater burden on you to make better shots and to kill the bunny more quickly. The longer your dog is running the rabbit, the harder he works and the more tired he'll get. Be careful running him in hot weather for extended periods of time.
Don't feed him before you take him hunting. It isn't good for him and some dogs simply won't hunt on a full belly. If there is no streams, water sources in your hunting area, bring along some for your dog.
When you get a bunny, the dog will usually only be a short distance behind him. Get to the bunny before he does and make a big fuss. Let him smell the bunny and he can even mouth it a little, but don't let him tear/rip the bunny or you'll have a rabbit eater on your hands. Hold it up beyond his reach and he'll jump up excitedly, praise him for a good job, then stick the bunny in your game bag. Make sure you have some plastic bags or absorbent material to soak up the blood, otherwise you're goint to have a real mess on your hands. I generally take along a small backpack to tote the bunnies in, along with extra shells, snacks, compass, water, matches and first aid kit for me and the dog.
Don't let the dog eat any of the entrails. He can pick up tapeworms from them. Also, incidence of "Tularemia" an infectious disease found in some rabbits, is on the rise in some areas. You'll notice spots on the liver, etc... That's why it is a good idea to wear plastic or latex gloves when cleaning them. You can check out this by doing a net search or check out Beaglesunlimited.com. Great resource for beginner bunny hunters.
Hope this helps and feel free to drop me a line with any more questions.
