Child Custody Protection Act of 2019 This bill establishes new criminal offenses related to the transportation of a minor across state lines for an abortion. Specifically, the bill makes it a crime to knowingly transport a minor across a state line to obtain an abortion without satisfying a parental involvement law in the minor's resident state. A parental involvement law requires parental consent or notification, or judicial authorization, for a minor to obtain an abortion. A violator is subject to criminal penalties—a fine, up to one year in prison, or both. The bill provides an exception for an abortion that is necessary to save the life of a minor whose life is endangered by a physical disorder, illness, or condition. Additionally, the bill imposes criminal penalties on an individual who commits incest with a minor and knowingly transports the minor across a state line to receive an abortion.