Let me make you a tiny bit less comfortable. I just saw that you're based in LA, and since the AZ flight from LAX arrives at FCO at about the time indicated, some more info:
If you do arrive from LAX, you'll be arriving by bus or train at Term 3, and you'll be departing from the same terminal. Follow the signs to connecting flights. You'd also have to go through immigration, thus you'd have to add at least 30 minutes for all of the above. Assuming no delays, you'll still have plenty of time left. Walking to the D Gates located at the end of Term 3 will be about the same distance (5-10 min.) as from Term 1. But if this is the case, i.e. flying a TATL into FCO, I'd rather not check luggage, the risk of it missing the connection is much higher.