Laura was born Aiel, but was found (a-la-Rand style) by a young Saldaean woman of a minor House, who had been put out of the Tower for not having the strength to be raised, and her soon-to-be husband, who was Andoran. They took her to Saldaea after their marriage, where she was raised. The blonde/tall/green-eyed look was mostly just thought to be from her father's Andoran blood.
She grew up, mostly enjoying reading and such, and dancing, but one of her friends taught her the sword when her father wasn't around. She was good at it, almost a natural warior, but she disliked killing and war. She's a very un-emotional and logical person, and saw no use in fighting, except to keep back the Blight and Shadowspawn. She was dedicated to the Light above all else.
When she was 14, her best friend Kelleri grew deathly ill. As Laura was staying with her friend as she died, Kelleri sat bolt upright, and then fainted into a natural sleep. Laura's mother came rushing in, saying she had felt channeling, and it must have been strong for *her* to have felt it. The next day, Laura's friend was good as new, and a week later, Laura fell into an illness almost as bad as Kelleri's had been, but it was gone in just a few hours. Laura and her mother packed her up and sent her to the White Tower.
She went to the Tower, where she uncovered her Talents were that Fortelling, Dreaming, and Healing. Her strongest Power was Spirit, but she was also strong in Fire and Water.