If the rear axle has gear whine, you may be in need of a replacement gear set. First, make sure the axle fluid is at the proper level. If it's never been changed, change it out for some good brand name synthetic fluid. If you have an LSD (limited slip differential), youll have to add a couple ounces of friction modifier so the clutch packs don't stick.
Worst case, you have several replacement options. Yukon Gear & Axle
is my choice for parts. To have a shop rebuild the axle with new parts won't be cheap, but expect around a $500 bill. A second thing you could do is phone local salvage yards and get a whole new axle. Most have relatively low miles on them as they are generally salvage vehicles. If you have a 4x2 and want/need more oomph from the truck you can upgrade with a lower gear. If you have 3.73, you could upgrade to 4.10's for nearly the same cost while increasing performance.
I also can't believe the dealer didn't even suggest that the rear axle may be the culprit, and all they do is install spark plugs! Geeze.