Beast Master's Quest by Andre Norton
On the future frontier world of Arzor live several beast masters, people gifted with telepathy and trained to communicate mind-to-mind with teams of animals. Laris, a young, orphaned, ex-refugee who has the beast master ability, has made a home for herself with a family of Arzor ranchers, and becomes friends with beast masters Tani and Hosteen Storm. Laris has also bonded with an intelligent and mysterious cat-like creature named Prauo, and when she inherits a spaceship, she realizes that she might fulfil her dream of finding Prauo's home planet. Laris is able to convince her adopted family to embark with her on a journey into the unknown depths of space, but what she and her friends find tests their abilities and threatens their very lives. Laris can only hope that they will all get back to Arzor alive.