I am in Brisbane and it took months to find someone and get into them! I basically got there by googling until I hit on those who use natural thyroid as it seems they have a better pic of the whole T4/T3 importance for those who do not respond well to just T4, though a lot of people work well on this alone I believe.
.25 is apparently a "nothing" dose, .50 is a starter dose as per info available here. Did you go straight to .100 or ease into it and how long have you been on that, I am guessing a while as in the 6 weeks and your retest is what you showed in your bloods?
I take adrenotone which is a doc. Prescribed adrenal support supplement via metagenics in oz but there are OTC ones as well along with calcium, zinc, magnesium and selenium all of which support the thyroid and supposedly help at cellular level BUT I have had these recommended by the doc as my bloods showed a need for them, especially zinc and magn. And I have recently learned that using Brazil nuts for selenium instead of a supp. Can cause side effects due to not knowing how much you are actually getting so I only take what I am advised to take by the doc. Perhaps a naturopath or holistic person could guide you on that side of things if you get no response from your doc.
The docs name Martin hill who uses natural hormones is in Melbourne I think, perhaps look it up and see if you can get in without referral, or even with referral from your own doc. We are all entitled to a second opinion, even in Australia!