Just an odd thought. Mab would have to change the identity she uses in the mortal world from time to time. It would look awfully strange if her law degree was from the 19th century or the early 20th century.
I did a little research and the first female lawyer in the U.S. was a woman named Arabella Mansfield; and she was admitted to the Iowa Bar in 1869. In the UK, the first woman to "be called to the bar" was one Ivy Williams in 1922; though she never practiced law. The first women to practice as a barrister in the UK was called to the bar a few months later. Her name was Helena Normanton. In France, the first woman to be allowed to act as an attorney was one Victorie de Villirouët, during the French Revolution in 1797-98; though it would be another 102 years until another women would legally be allowed to do the same thing in France. She successfully defended her husband against a charge of treason. If Mab had been there; well, I picture her being a prosecutor rather than a defender.
I recall Mab used the last name Summerset in Summer Knight. That was a reference that the Summer Solstice was almost at hand, a harmless play on words. However; with the injunction the fae have against telling direct lies, I think there would be a stricter code for Mab to follow in doing something as formal as becoming an attorney. There are many names which Mab has been given in different folklore and literature, so I think any name she practiced under would at least be a reference to her actual identity.
One other passing thought. I wouldn't like to see Mab have the time to become a judge in any type of mortal court. I picture her as a "cut the baby in half" kind of judge, only she would really mean it.