The Rowan by Anne McCaffrey

Rowan, a telepathic, telekinetic three-year-old, is the sole survivor of a mining disaster on a frontier planet. As she matures, her powers grow until she becomes one of a handful of "Primes" with the Federal Telepath & Teleport network, the organization responsible for telecommunications and shipping of cargo throughout the galaxy. Rowan finds herself alienated from humanity and her coworkers due to her unique talents and tremendous responsibilities until she senses Jeff Raven, a fellow talent, on the fringes of explored space.