It's all up to your own risk tolerance. We've frequently flown in the day of the cruise and have never had a problem. Just go with whatever you feel comfortable with. If you're particularly worried, you may want to look into travel insurance.
We have never booked air through the cruise line. I just can't justify spending 50% more for a third-party ticket with less convenient flights on airlines I would never pick myself.
(And as someone who detests Florida, I view any extra time spent there as lost time I'll never get back.)