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For some children, even minimal exposure to dogs can trigger sneezing as well as other more serious respiratory problems. According to Healthy Children, it's estimated that10 percent of kids are allergic to animals, but when it's your child begging for a puppy, it's hard to say no. Pet Education reports there are no hypoallergenic dogs, but poodles, terriers and schnauzers have less dander and therefore a better record of allowing kids with allergies to enjoy them. Many of these dogs are particularly suited to homes with children.