National cemeteries fall under the VA, not the DoD.
38 CFR 1.218 (a)(13) prohibit the carrying of firearms (openly or concealed), explosives or other dangerous or deadly weapons while on VA property, except for official purposes, such as military funeral honors.
(b)(37) Possession of firearms, carried either openly or concealed, whether loaded or unloaded (except by Federal or State law enforcement officers on official business, $500.
https://www.law.cornell.edu/cfr/text/38/1.218
38 CFR 1.218 (a)(13) prohibit the carrying of firearms (openly or concealed), explosives or other dangerous or deadly weapons while on VA property, except for official purposes, such as military funeral honors.
(b)(37) Possession of firearms, carried either openly or concealed, whether loaded or unloaded (except by Federal or State law enforcement officers on official business, $500.
https://www.law.cornell.edu/cfr/text/38/1.218