Women and Countering Violent Extremism Act of 2019 This bill (1) authorizes assistance to women's groups in foreign countries that work on terrorism-related issues, and (2) amends various reporting and training provisions to incorporate issues related to gender and terrorism. The President may provide assistance to non-U.S.-based, women-led organizations countering violent extremism and terrorism in foreign countries. The President's periodic Women, Peace, and Security Strategy shall include a section on (1) women's contributions to countering violent extremism, (2) preventing women's involvement in violent extremism, and (3) the gender dimensions of disarming and reintegrating former extremists. Training for certain personnel of the Department of State and the Department of Defense (DOD) shall include training on preventing violent extremism. The State Department shall seek to double the number of women receiving training under its Anti-Terrorism Assistance programs within three years of this bill's enactment. The State Department, DOD, and the U.S. Agency for International Development shall conduct research on gender and countering violent extremism, including best practices to support women preventing violent extremism, and utilize the results of such research in their programs. The State Department's annual country reports on terrorism to Congress shall include, for at least five countries, a gender analysis of the conflict drivers, power dynamics, and impacts that are relevant to violent extremism.