Women's Health Protection Act of 2019 This bill prohibits state or local governments from imposing certain restrictions on access to abortion services. Specifically, state or local government may not require unnecessary tests or procedures in connection with the provision of abortion services, the same health care provider who provides abortion services to perform such tests or procedures, providers to offer medically inaccurate information to patients before or during abortion services, providers to refrain from prescribing certain drugs, certain hospital facility transfer agreements, one or more medically unnecessary in-person visits, or patients to disclose the reason for seeking abortion services. The bill also prohibits limitations or requirements that both single out and impede access to abortion services based on a number of factors (e.g., restrictions that are reasonably likely to decrease the availability of abortion services in a state). A state or local government also may not prohibit abortions prior to fetal viability nor prohibit abortions after fetal viability in cases where the health care provider determines that continuing the pregnancy poses a risk to the patient's life or health. Additionally, the Department of Justice, individuals, or health care providers may bring a lawsuit to prospectively enjoin a limitation or restriction that is prohibited by this bill. The bill further requires the government defending such a limitation or restriction to show that (1) it significantly advances the safety of abortion services or patient health, and (2) such advancement cannot be met by a less-restrictive measure.