I would say yes, once you've passed the residency time period.
Some states require notification of a move within the state during a certain time period in order for their permit to remain valid. It is not too hard to imagine that an out of state permit wouldn't necessarily be recognized within your state of residency in lieu of possessing a valid permit for your home state.
Further, I believe Florida, for reciprocity purposes, only recognizes permits from other states if the permit-holder is a resident of the state issuing the permit. Since you possess a non-resident Florida permit, I'm not sure how this would affect the validity of your permit in the state of Florida.
My best guess would be to just be on the safe side and get your KY permit. My responses here should be worth exactly what they cost you, so check with the authorities.