I can't help with Adelaide, I am sorry, but I found Head Covers (it's a Canadian firm) good, not too expensive and very quick to deliver - everything as I had ordered. The soft "straw" hats were great (with summer coming) and I still wear them!
www.headcovers.com. ;
Most people find hair goes within 2 weeks of your first chemo, give or take a day or so. Your scalp may get tingly, or sore beforehand as the hair follicles are affected. It made losing my hair easier as I didn't like the feel of it at all (it looked OK though). I got it cut very short before it started falling - less mess! Best wishes.