Same problem on 2011 model.
I have a 2011 quad, 2wd and 4.7. It has the same rear brake shake that frustrated me on the 2005 I had.
I changed the front rotors with Centric slotted and powwrstop pads. Also installed new rear drums, shoes and hardware. Problem is 95% gone but you'll still feel a mild shimmy in the rear after driving a while. Tolerable but not ideal.