Does Qantas offer the same perks at their elite levels as does AA...ie EVIP's etc?
In Australia, only Virgin Australia offers an equivalent to EVIPs (or SWUs), but they are more limited than what you would be use to with AA. Top status at Virgin Australia gets 4 complimentary upgrades per year, but these can only be used on single sector domestic flights, and only for "flexi" fare tickets.
Qantas does not have an offer similar to EVIPs.
(The Qantas free "upgrade credit" program is long dead and buried.)
Qantas has extensive domestic market share and IMO lost the impetus to “do more” for customers years ago, in recent times they have been slowly and systematically cutting back on “elite privileges”* to cut costs and leverage their market dominance. (*the most recent perk to go, seems to be access to BA business class lounges for Qantas Club members, the Qantas equivalent of Admirals Club).
Virgin, on the other hand, has been systematically looking to "do more" for customers in recent times, in a bid to increase their market share. Virgin Australia recently had a status match, officially it is over, but if you want to contact them directly and explain your situation, they may be willing to do something for you, depending on your anticipated level of flying? (note: Virgin's domestic lounge network is smaller than that of Qantas. But EXP will get you into Qantas lounges when flying on Qantas anyway.)