Connecting Flight from Rome (FCO) to Palermo (PMO)

What you are describing is essentially the same as leaving the airport and coming back. When we went to Sicily we flew to Rome, spent a couple of days there, and continued on to Palermo. We did did a similar thing on the return trip, flying from Catania to Rome, staying overnight, then flying home.

Since your Palermo flight isn’t booked on the same ticket as your Rome flight, you are correct that you will need to go through immigration passport control because you are entering the Schengen zone, then collect your luggage and go through customs. Then you will need to check in for your Palermo flight, checking your luggage if you are not carrying on, go through security and then find your gate for the Palermo flight. All of this will take time. I don’t think it would be wise to book the 11:55flight.

Book a later flight. If everything clicks and you're at the check-in counter well before 11:55, ask if they can move you to the 11:55 flight at no cost. If there are empty seats, European airlines will sometimes do this in hopes of reselling your seats on the later flight. No guarantees though.

If wanderlust (or I) do NOT have bags to pick up and recheck, could that person make the 11:55 more comfortably? (Thank you, wanderlust, for raising the question!)

What if you first flight is delayed?
I did the Rome to Palermo this past march, and chose a mid-afternoon flight. My flight was on Alitalia and I paid to use the Alitalia lounge (maybe 35€?) for my wait. Not the fanciest lounge, but they did offer coffee, food, and showers.

You could do it, IF everything clinks. Our experience with immigration in Rome has run from 30, 45 minutes to over two hours. You cannot control that. In a similar situation two years ago we lost the second ticket because our original flight from the US was canceled and we did not get rescheduled until two days later. Rare, but it happens. So you need to have a plan B. I personally would not book a flight that tight.

Thanks everyone for the responses! The 11:55 is cheaper, and on a different airline than the later flights, so I won't be able to try to get on the earlier flight if I do have enough time.

Most likely I will do carry on, on the flight into Rome, then check it on the second flight. My bag is an American carry on size, but I think it's too large to carry on, on the smaller budget European carriers. I thought I might save some time there, but I think I still might be cutting it too close.

Wanderlust,
A agree with the others, it’s a gamble mainly because of possible unforeseen delays that you may encounter.
Do consider staying at least an overnight at your arrival city before heading to Palermo.

Last month I flew to Milan, got over jet lag while exploring this great city for a couple of nights, then I flew to Palermo.
I did the same when I flew back from Catania.

When I arrived to Palermo I took the bus into the city, although I’d considered taking a private transfer arranged by my B&B.

Sicily is amazing, enjoy!

There's a 11:55 flight that I was hoping to book, but I'm afraid that will be cutting it too close.

Your fear is well founded.

Not saying it cannot be done, but you need Swiss watch precision and efficiency of every step of the trip to make it work.
Like in the Dirty Harry movie, you need to ask yourself "are you feeling lucky...?"

Are these flights in different terminals?

Two years ago I had a separate ticket on Alitalia for Rome to Càgliari at 1:30 because I was worried that my flight would be late and I would miss the 11:45 flight. My flight arrived early and I did what Frank suggested. I went to the Alitalia counter and politely asked if I could change flights at no charge. They checked the flight, saw there were a lot of empty seats and changed the ticket. So book the later flight and if you arrive with enough time, ask.

That does not works for the situation. The OP is saying that the the 11.55 flight is the only flight. Cannot book a later flight.

What I did in this situation is book two tickets from FCO to PMO - one three hours after my scheduled Rome arrival, and one ten hours after my arrival. I knew I'd be using one and throwing away the other one, and the combined price of the two tickets bought in advance was still cheaper than a last minute ticket on my travel date (a Monday). In the end, I made the three hour "connection" with plenty of time to spare, and I was dealing with checked luggage. But of course that's not guaranteed.