12 weeks old:
Rabies. The age to receive the rabies shot is approximate. Most town/cities/regions have laws for when dogs must receive a rabies shot, as this disease is highly contagious and deadly. *Leptospirosis, for dogs that are at risk.
Your dog will usually need a combination vaccine and what goes into the shot will depend on that dog's particular health risks. For example, a shot to guard again Lyme disease if you live in an area where the risk is high and your dog is outside often. A second * Leptospirosis, for dogs that received the first one at 12 weeks.
16 weeks: * Leptospirosis, 3rd and final inoculation for puppies that received the first 2 at 12 and then 14 weeks.
* Leptospirosis - This vaccination is a voluntary one and one that owners should put serious thought into. It protects Beagles from the extremely serious Leptospirosis disease caused by the bacterium Leptospira interrogans. It is usually transmitted via urine of wildlife. If your Beagle has any access to land that could be home to squirrels, wild hare, deer, raccoon or other wild animals, it would be prudent to have your dog receive this.
The only shot absolutely needed when your Beagle is an adult dog will be for rabies, and this is per the law of the region that you live in. However, depending on lifestyle, activity and environment, booster shots should be recommended by an experienced veterinarian, but not demanded. If you do have a trusted vet, it is suggested to take his advice to keep your dog healthy.