PITTSBURGH—Amber, a canine athlete, recently won first place in an agility competition, narrowly beating out Daisy, a Chihuahua, in the 4-inch-tall category. The 3-year-old, four-pound Yorkshire, who wore a ribbon in her hair for the event, cleared several hurdles and tunnels, zigzagged through poles and traversed a teeter-totter at an average two yards per second in a race against the clock. Amber's owner credits her success to practice and mentoring from a family member, Tiffany, who competes in the 8-inch category and has several titles, including Teacup Agile Dog Champion. "Amber just follows everything Tiffany does," says Phyllis Bandi, who...