Been searching for flights from Rome to Santorini for 26 April 2016. There are award flights available through Air Berlin/Niki routing via Vienna, with availability shown on AA.com.
Is it possible to book using Qantas points via phone?
Yes, you just call Qantas Frequent Flyer and feed them the dates / flight numbers you are after. They will probably unfortunately add a phone booking fee. I haven’t ever looked for AB flights on Qantas.com so assume you have tried that already and they are not showing.