DOTGOV Online Trust in Government Act of 2019 or the DOTGOV Act of 2019 This bill transfers the .gov internet domain program from the General Services Administration to the Cybersecurity and Infrastructure Security Agency (CISA) and provides support for expanding .gov usage among public entities. The bill directs CISA to make .gov domain name registration services, as well as supporting services, generally available to any federal, state, local, tribal, or territorial government entity, or other publicly controlled entity that complies with the requirements for registration developed by CISA. Total fees collected for new .gov domain registrants or annual renewals of .gov domains shall not exceed the direct operational expenses of maintaining the .gov internet domain. CISA shall inventory all host names and services in active use within the .gov domain and provide the data to domain registrants at no cost. CISA shall develop and submit to Congress (1) a strategy to utilize information collected for countering malicious cyber activity; (2) an outreach strategy to local, tribal, and territorial governments and other publicly controlled entities to inform and support migration to the .gov domain; (3) a .gov domain security enhancement strategy and implementation plan; and (4) the development, assessment, and determination of the amount of any fees imposed on new .gov domain registrants or annual renewals of .gov domains. The bill allows recipients of State Homeland Security grants or Urban Area Security Initiative grants to use grant funds for migrating any online service to the .gov domain.