You can bring your pets into Italy. There's no requirement for quarantine if you have documents issued by a veterinarian that certify their place of provenance and their good health. Where dogs are concerned, the documents must also state that the animals come from areas which have not seen cases of rabies over the preceding six months. Once in the country, the animals must be registered at the Dog Registry (Anagrafe Canina). Check with the Italian Consulate at home before traveling with your pet.