We can't get plates anymore because (at least in Minnesota), if the person with a disability is over 18 they must be the principle driver or owner of the vehicle to get plates; DD is neither. When we did have plates, we also had a hangtag.
I agree with the others. There is not a way for you to get a handicapped permit from Florida - those are only available to residents. But, you very well may be able to get a hangtag from your home state. Since you already have license plates, you might be able to just call up and get a hang tag without filling out any more forms.