Go somewhere else! $1,200 should get you a lot more than just gears and labor. Without knowing your abilities, it is hard to recommend whether to do it yourself or not. I did my own with no experience, but I read a lot of books, recorded about 7 different rebuilds on various TV shows and then watched them about a thousand times and then had at it. So far, so good. It's really not that hard if you just take your time and double and triple and quadruple check that you stay within specs (backlash, etc.). Randy's Ring & Pinion has a great book that will walk you through the process.
Figure for expenses:
$150-200 for quality ring and pinion.
$80 for master rebuild kit.
$20 for new gear oil.
$400-600 for labor.
At best you're looking at under $1,000 to have it done, or you can do it yourself. Even with labor, for $1,200, you should be getting close to the price including a cheap locker.
Like both Cox and Rosco mentioned, check around. Check the gears or get a 2nd opinion. If it is the gears and you decide to have someone else do the work, then do your homework. In addition to varying prices for labor, I know a lot of professional mechanics who don't check backlash and simply re-install the original shims. If you're ok with that, then great. If not, make sure the shop knows how to set up gears properly. You'll be amazed how many don't.
Good luck!