You should be open with your head. It sounds as if you have a good working relationship. Any head will know that ambitious staff will expect to move on after a period of time. If you have your head on side from the start, she may be able to steer you in the direction of your next job by using her experience. Discuss your career intentions with her and don't risk her finding out when a colleague mentioned your name informally at a meeting.
That would be a greater risk to your working relationship, particularly if you didn't get the job.Honesty is the best policy in the long run.