Gordy,
They do let you hunt and fish on the Eglin Reservation. It's about 475,000 acres and about half of it is open to the public. The rest of the reservation consists of active bombing and test ranges. I live and hunt near the Navy Explosive Ordnance Disposal school. Some days while hunting you will hear some really big blasts. They don't seem to bother the wildlife. They get used to it. It does freak out my dog though. She usually looks for a bed to crawl under.
Here is the info from their website:
For information on hunting, fishing, or other outdoor recreational activities on the Eglin Reservation, contact the Natural Resources Division (locally known as Jackson Guard) of the Environmental Management Directorate Division.
The Natural Resources Division can assist you with necessary permits, information and copies of the most updated Outdoors Activities Map and Regulations. These brochures show the open and closed areas of the reservation as well as current rules and regulations.
Fees are charged for hunting, fishing, camping, chopping firewood, and other outdoor activities such as cycling. Hunting and fishing permits are available at a reduced rate to persons age 65 and older with proof of age and 100 percent certified disabled persons.
When ordering permits by mail, please allow three weeks for delivery. Send your requests to: Natural Resources Division, ACC/EMSN, 107 Highway 85N, Niceville, FL 32578, specifying the number and type of permits desired together with the proper payment and proper identification, or a copy of anything with a date of birth on it. Payment should be made by money order, certified or cashier's check payable to AFO Eglin AFB, Florida. Personal checks are also accepted, with proper identification.
The Natural Resources Branch of Eglin is open Monday through Thursday from 7:00 a.m. to 4:30 p.m., Friday from 7:00 a.m. to 6:00 p.m., and Saturday from 7:30 a.m. to 12:30 p.m. only. They are closed on Sundays and all Federal Holidays. Information may be obtained by calling Jackson Guard at (850) 882-4164 or DSN 872-4164.
http://www.eglin.af.mil/newcomers/leisure.htm