Fairness for Korean DMZ Veterans Act of 2019 This bill extends the presumption of service-connection for certain diseases associated with herbicide (e.g., Agent Orange) exposure to veterans who served in or near the Korean Demilitarized Zone between September 1, 1967, and August 31, 1971. Under a presumption of service-connection, specific disabilities or diseases diagnosed in certain veterans are presumed to have been caused by the circumstances of their military service. Health care benefits and disability compensation may then be awarded.