With the airport being so close to the cruise port, I think you will be fine. Just make sure to let Princess know you have an early flight and you should be one of the first ones off the ship, there is usually a form you'll need to fill out before the end of the cruise,
I wouldn't bet on it with the heightened security and the threat level being raised. You'll probably get off the ship alright, but you might get held up at the airport. There are long lines again at our local airports...even outside as every car is checked.
If your flight is out of Fort Lauderdale, 11:45 should be okay because the airport is only five minutes from the pier at Port Everglades. If your flight is out of either Miami or West Palm Beach, change it -- you'll need extra time.