Is 1 hour stopover enough at FCO for flights within Italy?

If you haven't purchased your ticket.....have you considered the train? Under four hours with one change. Total travel time with the plane, considering you have to get to the airport two hours ahead of time, is over five hours.

Omio site says "No trains." Trenitalia site lists only 6 hour ride options. Rome2Rio site says "No trains listed." However, my date of travel is May 25, 2024, so train tix may not be bookable/listed as yet. Do you think that's the case, and I shouldn't worry?
Thanks!

Too early
You can check same day of week now to see probable options in May 2024

No need to worry, there will most likely be trains in May in around 4 hours. Check Trenitalia again in January. Flying between the cities would be silly.

You can check same day of week now to see probable options in May 3024

That far away, anything is possible. The options then might be completely different from the options today :-)

Way too early for train tickets. As stated, the May schedules probably won't be available until early 2024.

I also think it is way too early for plane tickets but you may think differently.

Don't use Omio, but the actual train operator, Trenitalia, https://www.trenitalia.com/en.html
Right now, there is one direct train on Saturdays at 7:05 am, taking 4 hours and 10 minutes to get to Naples. There are faster trains later in the day requiring a train change in Caserta in as little as 3 hours and 43 minutes. Trains will show up on the schedule after December 9 and may not be bookable until later.

PS, I see that the 1 hr connection time itinerary is the fastest Bari-Napoli flight time of 3 hours. Considering that you will have to be at the airport at least 90 minutes before departure, and you will end up at Napoli Airport and still have to make your way into the city, it will be over 5 hours to get there and cost at least 100 EUR. Even Base Fare on the direct train is 36 EUR (48 EUR 1st class) and less if you buy a nonrefundable ticket in advance.

Thank you everyone for weighing in. I'm going for the train! Cancelled the flight. Grazie, grazie...

Good call..IMO I would swim b4 I will take ITA again! The train sounds wonderful!