Global Brain Health Act of 2019 This bill establishes programs to provide international support to address (1) autism spectrum disorders (ASD); (2) hydrocephalus (i.e., the accumulation of fluid in the brain commonly occurring in infants and young children); and (3) Alzheimer's and other forms of dementia. Specifically, the U.S. Agency for International Development must establish the Global Autism Assistance Program to (1) support local service providers and advocacy groups focused on ASD in developing countries and (2) train parents and teachers who work with children with ASD. In addition, the President is authorized to provide foreign assistance to (1) support hospitals treating hydrocephalus in developing countries, (2) establish at least 20 hydrocephalus treatment centers, and (3) develop surgeon training programs. Further, the Department of Health and Human Services must collaborate with the World Health Organization to establish a Global Alzheimer's Disease and Dementia Action Plan to (1) conduct clinical research, (2) raise public awareness, and (3) support prevention and treatment of Alzheimer's and other forms of dementia.