Well, if you don't get per diem, then you shouldn't get charged for staying in the Q. Although NAS Whiting and NAS Pensacola are in the "same geographical region," the two are not close to each other. That would be comparable to having orders to a ship here in San Diego with a Duty Under Instruction stop up at Camp Pendelton. In fact, the driving time is greater when going between Whiting and Pensacola than between San Diego and Camp Pendelton. In any event, you should be compensated in one fashion or another. Whether the Navy wants to call it Per Diem or something else entirely is of course up to them.
--Steve