If she wants a purebred dog, the Bichon Frise would be perfect for her. Small, non shedding, and generally a delightful little dog. I always say that the Bichon will be my next dog, but when the time comes, it will probably whatever dog is there when I go into the shelter. Your grandmother had a poodle mix before and you might be able to find another at a shelter or rescue site. Just look for the curly coated dog. That is your best gage in determining if a dog will be "non shedding". Margarete is correct about Schnauzers as well.