How do I convince my Dr. to test me for hypothyroidism?

I have been trying to get treated for Hypothyroidism for over a year now. I'm American, currently living in Australia, but have been to many different professionals (Dr. or GP if you live here, naturopath, nutritionist, exercise physiologist...) and all of them have hesitated to refer me to an endocrinologist. My Dr. would only test my TSH and it was only slightly in the normal zone so she didn't test my T3 or T4. Finally... about 8 months ago now, an anti-aging Dr. ordered blood tetst that revealed I had Hashimoto's Disease but failed to treat it and prescribed me bio-identical hormones instead to treat adrenal fatigue.
I'm wondering if anyone has had the same experience and how you can go about persuading your Dr. to test and treat hypothyroidism... even if it's only the symptoms and not the blood tests?
In my case my blood test did reveal anti-bodies, but I'm still getting the run-around... what do I do?!
Also, if anyone has a GP in Perth, WA that treats this, let me know. All of the ones I have tried (about 10) aren't currently taking on new clients or referrals.