Pet travel insurance isn't a legal requirement to bring a pet into Italy, but it's genuinely worth arranging for any trip longer than a few days — emergency vet visits in Italy are not free, even for residents, and most standard home pet insurance policies don't cover veterinary care received outside the pet's home country.
Look specifically for a travel-specific add-on or a standalone short-term pet travel policy with EU coverage, rather than assuming an existing pet insurance plan already includes it. The claims process usually works in reverse of what people expect: the clinic gets paid upfront by the owner, and the claim for reimbursement is submitted afterward, with receipts and documentation. It's worth travelling with a payment method that has enough headroom to cover this, plus digital copies of a pet's medical history in case a new vet needs quick context.