Awareness of celiac disease in this pasta-laden country is surprisingly good, with roughly one in a hundred Italians on gluten-free senza glutine diets. Many restaurants have celiac dishes or even menus; there's a helpful list of them at www.ristorantiperceliaci.net and another put out by the Italian Celiac Association.
Admittedly, it's harder to navigate a gluten-free diet in the pizza-and-pasta south than in the north, where you can always opt for a risotto, something with polenta or grano saraceno (buckwheat) or chick pea-based dishes like farinata (though some recipes for this have wheat flour, too).
Image by Serviagricolo