I'm very sorry to hear of the situation. How old is she? What kind of doctor is she seeing tomorrow? Has she previously been assessed? If so, by who and what was the diagnosis? How long has this been happening for? Has she by chance been the victim of a significant trauma?
Ok, well you can assess his competence a few ways. Firstly, check that he is a registered Clinical Psychologist through AHPRA here http://www.ahpra.gov.au/Registration/Registers-of-Practitioners.aspx. Self harming/cutting is certainly a clinical problem and it is important that he is a Clinical Psychologist and not a Counseling Psychologist. Secondly, ask him about his experience with assessing and treating self harming. Self harming is usually associated with Borderline Personality Disorder (BPD) - a set of difficulties that sometimes develop in people who experience significant trauma/loss during their child and teenage years. If he diagnoses BPD then it is important that he has specific experience in treating BPD. The recommended treatment is Dialectical Behavior Therapy (DBT) and this requires specific training. If he isn't trained in DBT or doesn't have experience in treating BPD then you may wish to consider asking for a referral to someone more experienced. Thirdly, raise your concern with him directly. It is very reasonable for you to discuss this matter and you should at some stage ask him if he believes he is the right person to be treating your daughter. Psychologists are required to be aware of their professional limitations and not practice outside these. If he is a professional person he will quickly acknowledge any potential limitation and discuss an alternative with you. Lastly, you may wish to consider how many years he has been working since becoming a registered Clin. Psych. In my opinion (and as a very general statement) Clinical Psychologists usually begin to develop real expertise after about 10 years practice. There are of course exceptions to his but it you may wish to consider this as well.
I should note here that I am in no way saying your daughter has BPD as I haven't assessed her. I'm just offering BPD as an example and if he diagnoses a different problem then you should directly query his training and experience relative to his diagnosis.
I hope this has been of some help. Please let me know if you have further questions or would like me to clarify any part of my answer.