"An application for initial admission, change of status or extension of stay in E-3 classification, however, may not be denied solely on the basis of an approved request for permanent labor certification or a filed or approved immigrant visa preference petition."
It's not explicitly dual intent but the memo makes it clear that they won't kick you out for pursuing PR.
Kicking someone out of a country for deciding that they like working there and would like to stay permanently should fit everyone's definition of weird.
(I am of course aware that it is standard practice in the immigrant fearing bureaucratic world we live in today.)
Yes, applying for permanent residence with an E-3 visa is possible and not prohibited by dual intent. I successfully did this and there were no problems.
http://www.uscis.gov/sites/default/files/USCIS/Laws/Memorand...
"An application for initial admission, change of status or extension of stay in E-3 classification, however, may not be denied solely on the basis of an approved request for permanent labor certification or a filed or approved immigrant visa preference petition."
It's not explicitly dual intent but the memo makes it clear that they won't kick you out for pursuing PR.