Her name indicates that she was from Cairhien.
Doniella was a quiet Amyrlin, not particularly strong, but not in the control of the Hall, either; her benign neglect did leave the Hall pretty much in control of the Tower.
Doniella quite voluntarily resigned as Amyrlin in order to spend more time on her loved studies. She spent the next thirty-one years studying happily, however, she was not allowed to return to the Tower and was strongly discouraged from letting anyone know that she had been the Amyrlin Seat.
Doniella was also a Dreamer who made important studies on the Prophecies of the Dragon; in particular she made comments on the Termendal translation of the Karaethon Cycle, apparently so diffuse that they became "the subject of nearly as much discussion among scholars as the Prophecies themselves."