She is plump.
She is younger than eighteen. We know this because this is the upper age limit Verin set for girls that tested positive for the channeling ability. She is from Emond's Field or close by.
Barran seems to be a common name in the Two Rivers, especially around Emond's field. The following other Barrans are mentioned:
She is one of the girls that Verin Mathwin and Alanna Mosvani plan on taking to the White Tower to become novices. They only get as far as Caemlyn before hearing rumors about the White Tower Schism. She and the other girls stay with the Aes Sedai at an inn called Culain's Hound. Rand sees her there when he calls on Verin.