Any shop that charges more just because he see's a Vette badge is a BS shop. The Vette diff is not any more difficult that any other diff but the gear sets are a little costly. Once you have the diff on the bench the labor should be reasonable.
If that 1200 includes: Posi.. gears.. complete O/H kit and bench labor..Its a little high. If a posi was not included than it's too high.
If you wanna try it yourself get ya some parts and we can walk you thru it.