Logic would suggest that the sales should begin at the end of the financial year, but if there's one thing we've learned about sales events over the years, it's that logic is a precious and rare commodity! So you can expect Australia's EOFY sales to kick off in the weeks before June 30 (the official "last day" of the financial year) and then keep running for most of July.
Compared to the likes of Amazon Prime Day and Black Friday, the EOFY sales period is amorphous: it kinda just runs for as long as every individual retailer wants, and that can often be upwards of a month. So yes, it's probably worth waiting until June, at the very earliest, to make any non-essential purchases.