I've never done the Disney Transportation, but imagine that a 1:15 flight would be no problem at all. Generally, all passengers are off the ship by 9:00 am., and they have a ton of buses to get people back and forth.
We always take the DCL transfers. Yes, you should have no problems at all making that flight. I think you'll find that you have a couple of hours to kill at the airport. Our return flight is usually at 12:45pm and we usually do. As NCRedding said, they want everyone off the ship by 9:00am. It takes about 15 minutes or so to find your bags and go through Customs, then about an hour for the bus ride to the airport.
In 9 cruises, the latest I've been at the airport and through security was 10:15am, and that was in Dec. of 2001, with the extra-super-hyper-mega security, including armed National Guardsmen at the airports. We generally get off the ship between 7:30 and 8:00, depending on when they clear it. You could probably have a leisurely breakfast at the buffet and be among the last off the ship and still make it to the airport in plenty of time.
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