An osteopath is a doctor with orthodox training as well as training in the discipline of osteopathy (similar to chiropractic). I believe most are no more knowlegeable about adrenal fatigue than any MD, but I could be mistaken.
My first choice in doctors for the treatment of adrenal fatigue would be an ND (doctor of naturopathy). Many specialists, including endocrinologists, will miss a borderline case of adrenal fatigue. In general, they are looking for dramaticly low cortisol levels, or they don't consider it pathological.
Most ND's recognize how common adrenal fatigue is, and will diagnose based on a symptoms profile. Naturopathic treatments for adrenal fatigue are generally very safe and include diet change, herbs, and nutritional supplements. I understand that orthodox treatments for adrenal problems can be very dangerous if not done properly, so if you were to go that route for treatment it would be extremely important to get a definite diagnosis. But if you were to go the Naturopathic route, testing is not quite as important as the treatment is quite safe.