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Looking at my journal from our April 2010 cruise to/from Barcelona on another cruise line, I see that we disembarked our ship at 8:00 am and arrived at the airport at 8:30 am by taxi. The cost of the taxi was the equivalent of US$50 (40 Euro), so it comes out roughly even with the Carnival transfers if there are just two of you. So, it would have been doable for us, yet, there are some important considerations. First, we were on a ship that held fewer passengers, we were the only ship in port that day, and we had VIP disembarkation as we had sailed in a suite. We also lucked out with no traffic delays.
I'd be somewhat hesitant to cut it this close. We had a 1:30 flight to Heathrow, where we connected to a flight back to the States, and it wasn't so bad. But, as Dave noted, Carnival will transfer you if your flight is later than 9:00 am. No matter what you decide, be sure that you purchase travel insurance that covers you should you be delayed in getting to your flight.