At least you should not have snow or ice to contend with in FL
I would rent a car for the whole trip. Local transportation in the US, especially in S. FL. is no where as good as it is in Canada or Europe.
Quickest way from Orlando to Miami would be the turnpike. You can take I-95 but there has been some construction and traffic gets congested the closer you get to Miami, not to mention some of us in the Miami area don't know how to drive.
Driving from Miami to Key West, depending on when in the week, will take three to four hours. If there is an accident on US-1, the highway between Florida City and Key West then the drive time can be extended. Ensure you have a very good and current map, when driving in Miami.
I don't know how well Sawgrass is doing since a new, higher end, mall opened between Naples and Ft. Myers around 2005. Since then a number of customers who would bus in from Naples - Ft. Myers area now frequent the new mall.
Travel safe