I would also get Drs letter. I volunteer as a safe worker on a historic tourist railway (Guard and Signalman) which is an operational role. I have to have a medical every year a copy of my pathology reports. The letter is a very specific wording for Australia anyway. If you can go armed with a satisfactory letter, it will be impossible for them to worm out of that excuse. If you have been seeing an Endo for your treatment that will be much better than a GP or hospital staff Dr.
Good luck and let us know how you go.