Florida and Pennsylvania are both part of the Drive License Compact (DLC) so under this "one license" concept PA has likely already listed your FL violations on your current driver's license and thus your driving record.
As long as you have paid and properly taken care of the Florida tickets or citations it is doubtful that you would have problems obtaining a Florida driver's license. For more information on how to acquire a Florida license contact the FL Department of Highway Safety and Motor Vehicles.
Once you move to Florida you will need to get Florida coverage on your vehicle(s). FL coverage means the auto insurance policy is delivered or issued by an insurance company licenses by the FL Department of Insurance. Get your free car insurance quote from us.