The Case of the Missing Marquess by Nancy Springer

After the disappearance of her mother, 14-year-old Enola Holmes is determined not to allow her older brothers, Mycroft and Sherlock, to send her off to boarding school. Raised by an unconventional mother who largely ignored Victorian values, Enola has grown accustomed to freedom. She runs away to London in the hopes of reuniting with her mother - but finds instead a series of mysteries to solve.