Pet policy on Airbnb in Italy is entirely down to the individual host — there's no platform-wide standard the way there sometimes is with hotel chains. The listing's house rules section is the place to check for any pet mention, not just the amenities list, since many hosts only allow pets 'on request' rather than listing it as an open amenity. Messaging the host directly before booking is worth doing regardless of what's written, since policies aren't always kept up to date.
For dogs that need regular exercise, ground-floor properties, a fenced outdoor space, or a location close to a park are worth prioritising when comparing listings.