You can enroll your child in a Louisiana public school before you actually move to Louisiana, so the place is held while you are still at your old duty station. You do not have to prove you live in Louisiana up front, but you do have to provide that proof within 10 days of arriving.
Contact the school your child will attend and ask for advanced enrollment. Use the Louisiana Department of Education school finder if you do not know which school serves your new address.
Official military orders showing your reassignment to a base or duty location in Louisiana, the enrollment forms the school requires, and proof you live in Louisiana within 10 days of arriving.