Veterans' Education, Transition, and Opportunity Prioritization Plan Act of 2019 or the VET OPP Act of 2019 This bill establishes the Veterans Economic Opportunity and Transition Administration to administer economic opportunity assistance programs for veterans and their dependents and survivors. Specifically, the Veterans Economic Opportunity and Transition Administration must administer the following Department of Veterans Affairs programs: vocational rehabilitation and employment programs, educational assistance programs, veterans' housing loan and related programs, the Transition Assistance Program, and the database of small business concerns owned and controlled by veterans.