This is by no means an exhaustive list of Australian suppliers of art glass sheet, lead, solder, tools and other materials, but should help you in your search for somewhere close by. The larger companies mentioned here also have an online ordering website and will deliver anywhere throughout Australia. Most will offer fusing supplies as well as stained glass supplies. And here's a tip: many glass tools, sheets of art glass, even kilns for fusing or painting on glass do turn up on Facebook Marketplace or Gumtree.
There is also a Facebook Group called "Leadlight equipment buy and sell Australia"
You have no excuse: get started!

New South Wales

Australian Stained Glass Supplies have recently moved from Camperdown to Arncliffe. They still welcome walk-ins, but are more heavily weighted toward wholesale, online ordering and laminating. Note that they no longer run classes.
Clare Peters Art Glass Clare was actually one of my students at Finns Art Glass so many years ago I can barely remember... She and her husband operate a glass studio on the Central Coast of NSW, teaching classes in leadlighting and fusing and offering supplies by appointment. 0422151333
Leonie Le Cornu Stained Glass 141 Kingsway Cronulla 95239816 Leonie is charming and always welcoming of visitors. While primarily a production studio, Leonie also runs leadlight classes and sells most everything the hobbyist would need.
Penrose Glass at Kogarah recently underwent a significant shake-up of its business, but continues to trade and still has ample stock of art glass and leadlight supplies.
​Spectrum Art Glass 102 Adderley St Auburn 97370666 As well as stained glass and leadlight, Spectrum offer a large range of decorative glass options