Sabriel by Garth Nix.

Sent to a boarding school in Ancelstierre as a young child, Sabriel has had little experience with the random power of Free Magic or the Dead who refuse to stay dead in the Old Kingdom. But during her final semester, her father, the Abhorsen, goes missing, and Sabriel knows she must enter the Old Kingdom to find him. She soon finds companions in Mogget, a cat whose aloof manner barely conceals its malevolent spirit, and Touchstone, a young Charter Mage long imprisoned by magic, now free in body but still trapped by painful memories.

As the three travel deep into the Old Kingdom, threats mount on all sides. And every step brings them closer to a battle that will pit them against the true forces of life and death—and bring Sabriel face-to-face with her own destiny.