Delivering Optimally Urgent Labor Access for Veterans Affairs Act of 2021 or the DOULA for VA Act of 2021 This bill requires the Department of Veterans Affairs (VA) to establish a five-year pilot program to furnish doula services to pregnant veterans who are enrolled in the VA health care system. The program must furnish doula services through eligible entities by expanding the VA's Whole Health model to measure the impact that doula support services have on birth and mental health outcomes of pregnant veterans. The Whole Health model is a holistic approach that looks at the many areas of life that may affect health in order to make a health plan suited for each individual based on his or her health goals.