We did this recently, although our flight wasn't quite that early. But we took a taxi to Joe's Café at the Harbor Shops off SE 17th St - 1913 Cordova Rd. They open at 7am, so don't rush from the airport, since it's not more than 15 minutes away. For us it was only a 4 night cruise, so we didn't have full size suitcases, but we sat in one of the outdoor swings and were able to set our suitcases besides us. We had a leisurely breakfast - nothing fancy, but hearty and tasty.
There's a Publix a few doors down that sells wine, and past that is a Total Wine - I think they opened by 9am.
The Uber to Port Everglades was under 10 minutes.