Christine would know a few people for austrailia, but from OP's description her daughter's condition is likely going to require too much treatment to not be done by someone local. And your attempts to learn could be your best chance at resolving the issue.
There are as mentioned resources that can be used to learn, and there are 4 text's I generally recommend, they are:
Michael Bono's the Blend Method available at Texas Electrolysis Supply for I THINK $42
Electrolysis Thermolysis and the Blend by Hinkle and Lind
Medical and Cosmetic Electrolysis and temporary hair removal by RN richards available here: https://www.amazon.ca/Cosmetic-medical-electrolysis-temporary-removal/dp/0969474636
and Milady's Hair Removal Guide.( which seems to have been updates to Milady's Hair Removal Techniques) by Helen Bickmore, available here:https://www.amazon.ca/Miladys-Hair-Removal-Techniques-Comprehensive/dp/1401815553
I can also suggest the distance Learning program from Swansons Canadian Institute of Electrolysis, this will supply you with study materials and guidance, but you would still be advised to do practical instruction with someone nearby . You can contact Phyllis at swansons if you message me privately I can give you an email address.
Then there's the "tried and true " method of studying all this on your own first, and pestering the professionals here at hairtell when you have questions on details.
Blend is a good starting modality but it's not going to happen overnight. It will take time.Learning thermolysis is a little more doable when working on someone other that yourself such as in your case.
Regardless I recommend you take the dowagers advice and get to the bottom of the cause of the hair growth. If it is hormonal in nature this is correctable as was advised you. Spironolactone is one a variety of antiandrogen drugs used. Thyroid issues can also very commonly cause hirsutism. Getting to the bottom of the cause of the issue, is almost as important as removing the hair that is growing already.
Regardless, yes, given the conditions facing your daughter, I would be in support of your learning electrolysis. And dont be so hard on yourself about "starting with a face" . I think I spent about 6 hours practising on an arm , before attempting ( and then completing) my face. so it can be done, without the predicted scarring and maiming for life that many claimed I would have. But I would still start with blend until you are a little better with insertions but I think thermolysis is what is going to end up solving the problem for you. It a very precise skill to learn, so start with the blend first.
yell if you run into trouble.