They aren't best as they do shed, I would recommend a Bichon or a Maltese as they are hypo allergenic.! If your heart is really set on a Beagle then spend some time at a kennel and look after some Beagles to see if they upset your allergies - good luck!
Beagle shed a fair amount and are by no means hypoallergenic. However, there is no such thing as a hypoallergenic dog anyway. All dogs create dander, and all dogs shed. But, since the beagle is a relatively small breed it might actually create less dander than larger breeds. The only way to know is to spend time with beagles and see if you react. Some breeds that are better for allergies include: Basenjis, Yorkies, Schnauzers, Airedales, Wire-haired terriers and poodles. Hope this helps!
Web MD says: You may have heard that some dog breeds trigger allergy symptoms while others don't, or that short-haired dogs are safe while long-haired dogs prone to shedding are not. But on the whole, experts say that isn't the case. In fact, two dogs of the same breed can each give off very different levels of allergen. It's not the dog's hair or fur that's the real problem. Instead, people are usually allergic to the dander -- flakes of dead skin -- as well as the saliva and urine. So, no matter how long or short the hair, any dog can potentially cause an allergic reaction." The short answer is if you are allergic, you need to either avoid owning or living with a dog, or you need to treat your allergies. "Antihistamines, which block the effects of a chemical that triggers dog allergy symptoms; they're sold over the counter -- like Allegra, Claritin, Benadryl, or Zyrtec -- or by prescription. Some antihistamines such as Astelin are available as nasal sprays. Decongestants, which reduce swelling in the nose and relieve congestion; examples are over-the-counter Sudafed and Allegra-D. Other drugs, which affect allergy or asthma symptoms in different ways; prescription steroids -- such as Flonase or Nasonex sprays -- are a common treatment for allergies. Both Flonase and Nasonex are available over the counter and by prescription. Allergy shots are another option for people with dog allergies. They don't work for everyone, and a full course of treatment can take years. But they can really help some people with pet allergies. Talk about the pros and cons with your doctor."