Housing Choice Voucher Mobility Demonstration Act of 2019 This bill authorizes the Department of Housing and Urban Development (HUD) to implement a mobility demonstration program to enable public housing agencies (PHAs) to administer housing-choice rental-assistance vouchers in a manner designed to (1) encourage low-income families receiving such assistance to move to lower-poverty areas, and (2) expand access to opportunity areas. HUD shall require PHAs applying to participate in the program to submit a specified Regional Housing Mobility Plan.