Military member buying a gun on leave. Need some advice. Hello all,

I'm in the Army and currently on leave in Florida from Japan. 

I'm wanting to purchase a firearm but unsure of what proper paperwork that is needed to purchase one. 

I have a Florida DL but my address is not the same as my address listed as my home of record. 
My home of record and everything is in Florida just a different address than my DL. 
I also have my PCS orders to Japan but it is to my understanding that I would need PCS orders to Florida to buy a firearm with just PCS orders and my military ID(CAC CARD)

Any input is appreciated.