First and foremost, find a different Toyota dealer.

As said, they cannot tell you that the differential is bad via a simple test drive. Believe me, I'd munched rear diffs and all you'll usually hear is a slight whine that sounds like bad wheel bearings.

Look under the truck - in the center of the rear axle, on the front, where the driveshaft connects, is the differential. Does this part look NEWER than the surrounding parts (cleaner, shiny black)?

When I munched the diff on my 96 4Runner, Toyota would ONLY sell me a complete differential, not a carrier assembly as your bill states. The estimate was $1500 for the assembly. I can't believe they would charge you $1200 for anything other than a complete differential (called a third member, or in this case, carrier assembly.)

Where in TN are you? I'm sure people here could recommend some 4x4 shops that provide excellent service.