You need to use the EY site to see EY availability. It does not show on the AA site.
Go to etihad.com, select "Plan and book" from the top menu and then "Book with miles" from the dropdown. Then search. You are looking for "Guest seats" availability. If there is, then AA should be able to see it (although there have been reports in the past of AA in the US not being able to see availability but AA's Australian number being able to). It's important to remember that the number of miles and the taxes displayed on the EY site do not correspond with what AA will charge. Once you've found availability call AA, possibly even starting with the Australian number on 02 9101 9488.
Qatar from Australia to Europe with a transit (rather than a stop) in Doha will cost 60k/85k/115k in Y/J/F respectively.
This thread is best suited to your question:
http://www.australianfrequentflyer....couple-questions-aadvantage-newbie-59133.html.