A Christian woman should be allowed to wear a religious headscarf for her driver license photo. This is constitutionally protected under the First Amendment, which protects the right to free speech and the practice of religion. She is wearing her scarf for religious reasons, which is protected as a freedom on expression.
The freedom that the First Amendment gives to Americans includes beliefs and the right to exercise that belief. The main reason for a photo on a drivers license is to see the persons face. Covering her hair shouldn't be an issue whatever the reason, as long as her face isn't obscured.
Technically, freedom of religious expression is established by the First Amendment, but in the case of security issues, such as driver's license or passport photo, this can present a problem. I'm unaware of a legal precedent for these types of decisions, but I do recall a "Pastafarian" woman wearing a colander in her photo, and a court ruled this was acceptable. I imagine anything that conceals identity to an extreme degree may be subject to stricter rules, despite what the First Amendment allows.
While the first amendment offers protection against impeding religious freedoms, certain rules are in place for the protection of our society as a whole. The general public is not allowed to use any type of head wear. It is not a religion specific rule and therefor does not seek to impede any certain religion, but simply provide an accurate photo ID for public safety.