Moving along relative z axis with character controller?

Hi guys,

Essentially what I'm making is a hover-craft of sorts. I'm using both the Horizontal and Vertical axis for both the rotation and the up and down movement, relegating the forward movement to an acceleration button of sorts, in this case I'm going with the space bar. All is hunky-dory, except that there seems to be a problem with my script in that the object will move along the game world's Z, not its own. I know how to solve this with rigidbody, but I've found that using character controller is pretty handy for this game as the physics aren't exactly realistic. When I use axis for this, it works fine, so the problem appears to be in the Input.GetKey function.

Anyway, here is my script, hopefully someone has an answer for me?

 void Update () {
         CharacterController controller = GetComponent<CharacterController>();
         
             //move the object up and down
             moveDirection = new Vector3(0,Input.GetAxis ("Vertical"),0);
             moveDirection = transform.TransformDirection(moveDirection) * speed;
         
             //steer the object left and right
             transform.Rotate(0,Input.GetAxis ("Horizontal") * rotationspeed,0);
         
             //accelerate the object forward
             if(Input.GetKey(KeyCode.Space)) {
                 moveDirection = new Vector3(0,0,speed);
         }
             controller.Move(moveDirection * Time.deltaTime);