All states in the US have reciprocity with Florida. That means if you have a valid Handicapped parking permit in your home state, it will be recognized as valid in Florida too.
There are several things about the Handicapped Parking for the WDW parks that you should know, though.
1) If you are staying at a WDW resort, you will have the least walking by taking the bus when going to MK. If you park at MK, you still need to get from the parking area to the Ticket and Transportation Center (TTC). From there, you either take a boat or a monorail (up a long steep ramp to get to the monorail boarding area at the TTC and down one at MK).
The MK bus drops you off at the park, close to the entry turnstiles.
2) The regular parking lots are served by parking lot trams; the handicapped parking lots are not.
Some of the handicapped parking lots are very large and if you are on the end of a row or the back row of the handicapped parking, you will have a long walk to the park entry. If you don't have a wheelchair or
ECV with you, there are some courtesy wheelchairs available in the handicapped lots. There is no guarantee there will be one available when you get there though.
3) If you don't have a wheelchair or ECV with you, Disney actually recommends parking in the regular lot and using the parking trams if you are able to step up onto the tram and ride it. The parking lot trams leave you off the closest to the entry that you are going to get.
The parking lot CMs save parking spots on the end of the row closest to the tram stops for people with mobility disabilities.