Moving your pet to Italy is not too difficult. It can be a bit expensive however. If you have a really small dog or small cat, it can travel with you so long as it and the carrier is under 18Lbs. You will want to dig into airlines policy because not all will allow you to travel with a pet in cabin. It is possible to travel with your pet as checked baggage, but again that need research. For example, many airlines won’t let you check them if the temp is over 85 or under 40. Leaves out a lot of places.
The regulations are specific for importing a pet. This site gives the detailed breakdown.
We decided that we would use a pet relocation company. Our cat would not fit under the seat, and traveling with extra luggage AND a cat was going to make things complicated and chaotic. If you do go this route, get quotes from more than one company. The first company that gave us a quote was over $5,000 for our cat. Granted this included pickup and transport to the airport and then transport to our house in Italy, but wow! They did not give a breakdown, just a lump sum. I then contacted Happy Trails and they got back to me within a day, and provided a detailed breakdown of the price with the best case – worst case prices. (The airfare part cannot be specifically pinned down). They itemized the additional fees as well. Their price came out to 2500-3200. They listed optional transport from home to airport and airport to home which would come out to around 700 total. So even with the full service, they would be over 1000 less worst case, and we can easily see how much we would save/spend by adding or not adding the additional services. According to their site, they do a lot of relocation for military people and have special prices for service members.
Another place that gets recommended (at least in reviews) is Bliss Pets which we eventually used. The cost was approximately $3,000. It may sound pricey, but it was well worth it. They did an excellent job. They picked him up when they said they would, kept us informed with emails and pictures, and delivered him on time. Jessie, the cat, seemed no worse for the long trip, but he was very, very happy to see us!
Not a lot of people posting what they paid on forums, but from the little avail, it seems that 2500 on up is the norm for having someone ship your pet and handle all the paperwork.