Small Hypoallergenic Dogs and Which Breed of Hypoallergenic Dog is Right for Your Family. Taking care of any dog can be rewarding and fun. But there is a great deal of responsibility as well. Small dogs can require more attention from their owners, they cannot be left alone for more than a day, and they may have health problems as they age. Smaller dogs also do not require as much exercise as other breeds. Small dog breeds such as the poodle, maltese, shiz tu, and bichon frise are considered hypoallergenic because they do not shed as much as other breeds and they produce less dander.