1823 (adj.), "of or pertaining to Burma;" 1824 as a noun, "native or inhabitant of Burma," from Burma + -ese. Burman is older (1800 as a noun, 1802 as an adjective). Burmese cat is attested from 1939.
Entries linking to burmese
Burma
nation in Southeast Asia, from Burmese people's self-designation; see Myanmar.
-ese
word-forming element, from Old French -eis (Modern French -ois, -ais), from Vulgar Latin, from Latin -ensem, -ensis "belonging to" or "originating in."