Beale was suspended on Thursday pending a hearing into allegations he was responsible for sending offensive text messages regarding a team official in June.
His omission from Ewen McKenzie's squad for the Brisbane match offers Cooper the chance to play Test rugby for the first time this year after he missed the France series and Rugby Championship because of a shoulder injury.
McKenzie also included four uncapped players in wingers Tom English and Henry Speight, centre Kyle Godwin and prop Tetera Faulkner.
Fiji-born Speight, who qualified for Australia in September, will join the squad to familiarise himself with the set-up but will not be considered for selection as he continues his recuperation from a hamstring injury.
Number eight Ben McCalman has been ruled out for the rest of the year by a shoulder injury he sustained against the Springboks two weeks ago.
Luke Jones, who won his only cap against France in June, comes into the squad to reinforce the back row along with Jake Schatz.
Centre Matt Toomua joins McKenzie's long injury list after taking a knock on the head in the defeat to Argentina in Mendoza last week in the final match of the Rugby Championship.
Cooper, who last played for Australia against Wales at the end of last year's season-ending tour of Europe, underwent surgery on his shoulder in May and has impressed on his return to action in the National Rugby Championship.
The New Zealand-born 26-year-old started the last 10 tests of 2013 for the Wallabies but is likely to start on the bench behind incumbent Bernard Foley against the All Blacks at Lang Park.
The world champions are already assured of retaining the Bledisloe Cup after a 12-12 draw and 51-20 victory in their first two matches against Australia this year.
Forwards - Scott Higginbotham, Michael Hooper (captain), Matt Hodgson, Scott Fardy, Luke Jones, Jake Schatz, James Horwill, Rob Simmons, Sam Carter, Will Skelton, Benn Robinson, Ben Alexander, Sekope Kepu, James Slipper, Tetera Faulkner, Saia Faingaa, James Hanson, Josh Mann-Rea.
Backs - Israel Folau, Rob Horne, Joe Tomane, Adam Ashley-Cooper, Tom English, Henry Speight, Tevita Kuridrani, Christian Leali'ifano, Kyle Godwin, Quade Cooper, Bernard Foley, Will Genia, Nic White, Nick Phipps.