Dr. Graham Peveller is not a psychiatrist. He is a social worker with a Ph.D. in gender dysphoria and a few decades of experience working with the transsexual community both in the UK and in Thailand, and with working with Thai and USA based surgeons on pre-surgery assessment and counselling.
The Thai and USA surgeons regard his opinion very highly, and will operate based on his letter of approval, along with a short Q&A session with a Thai psychiatrist on the day of your surgery to make sure you are basically mentally well.
He's one of the people who surgeons such as Dr. Preecha of PAI or Dr. Saran will refer you to if you live in a country where there is no support for transsexuals, or where it would be illegal for a local doctor ot help you.
He is also one of a number of mental health professionals (including psychiatrists and psychologists) who help people who have been declined surgery by clinics such as Monash or Charing Cross to gain approval. Obviously, this makes him unpopular in some circles, and you will see this in some of the reviews online.
However, the fact that thousands of transwomen are now happily post-op and living great lives (I know several personally) following his approval should suggest that he knows what he is doing. Many of these people would not have obtained surgery otherwise, either because they did not meet some psychological profile of a gender clinic (e.g. being gay in their desired gender, or nor sufficiently feminine or masculine) or because they lived/live in countries like Malaysia or Qatar where gender transition and even cross-dressing is illegal.
If you work with Dr. Peveller, be prepared to spend a LOT of time documenting your life history and how you came to the decision to have SRS. Not seeing you in person, he will work a lot with the facts of your life, and he will make sure you have good logical reasoning and have come to this decision with considerable thought.
Also make sure you don't miss the opportunity to draw on his expertise as he has worked with many thousands of transwomen (and also transmen) in the past, and is happy to share his experience.
And if you want an opinion from someone local in Australia - feel free to contact me.