Qantas specific flights open 353 days in advance. Some sources says they opens at 10am. As of today it should open till 1/7/2017 (give or take 1 day -> I didn’t check to confirm). An easy way to check this for any airlines is to have a look as if you are booking a normal flight. What is the furthest date it allow you to select? You would notice a pattern if you check again the next day-> whether it opens one day at a time.
If you are flexible on flying non-Qantas One World airlines, you would have to check which other airlines partner fly to Greece and then check how many days in advance they open their flights. A quick check finds at least Qatar, BA, Emirates fly to Greece.
If you are hunting for premium (or any) award seats, it pays to check everyday as it gets closer to when the date in mind is open for booking.
Happy hunting. I had a hectic time myself in April this year.