If she doesn't have an under coat then she could be a Maltese Westie cross? That's what she looks like to me. Both breeds are single coat. Toby has food and environmental allergies (pollen). He is allergic to Chicken, Lamb and Fish, legumes of any kind as well. He is not only picky but he is very self regulating and will skip meals if he gains weight or won't eat if he isn't hungry. (Wish I had this problem.

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What brand of food are you feeding her? I have been using several different brands and switch between Rabbit, Turkey, Pork and Beef so he is less likely to develop an allergy to a particular protein.