You don't have to have a FL drivers license. We got our FL resident PAPs before we had our drivers license. We just showed them a utility bill with our name and Orlando address on it and a picture ID (our Texas drivers license). We also had Orange Co. library cards for our teenage sons because they had no ID.
From the WDW website it says:
You must provide any one of the following: Florida driver's license, Florida state-issued ID card (must have Florida address), current utility statement with your name and Florida address along with a corresponding picture ID, Florida voter's registration card with corresponding picture ID, a college ID for a Florida college, or a Florida-based military ID.