You can buy Louisiana hunting and recreational fishing licenses at resident prices while you are a nonresident service member on active duty, and so can your dependents. The license is valid only while the service member is on active duty.
Buy your license from a Louisiana Department of Wildlife and Fisheries vendor or online, and show a valid military ID at the point of purchase.
Your valid military or dependent ID card, which you also have to carry with the license while you hunt or fish.