We had that early flight out of Naples also. So glad we spent at least that one night in Naples. Loved the city and can't wait to go back! Our pension in Sorrento arranged a last minute taxi for us when our planned ferry trip looked too foggy. I think it was closer to 75 euro from Sorrento. I learned on the Amalfi coast that friendly hoteliers often have great contacts who aren't in anybody's books.
To Lulu, the early morning taxi ride from the historic center to the airport takes merely minutes. We seemed to be the only car on the road at 5:30AM, which got us to the airport WAY too early. Luggage was checked all the way through. No need to retrieve at Rome.
We stayed at the Decumani Hotel de Charme in Naples, a recommendation from this site. I was a little wary since Tripadvisor reviews were all over the map. The outside of the hotel is off-putting, but once you take the elevator up to their second floor lobby, it's really nice and the people were lovely. They sent us to a fun little cafe down the street -- Pulcinella -- and called a great guide who lived nearby. (Our RS guide cancelled at the last minute.) In only one afternoon and evening in Naples, a four hour walk around the city center with Adele showed us some of the best churches, the street of the prescepi, historic neighborhoods, and places to find memorable street food. My vote is definitely to go into Naples the day before.