Any 53 - 62 corvette differential will work or any 53 - 64 gm passenger car.
It is my understanding that these are not particularly strong rear ends. They are a 17 spline axle setup if I recall correctly. Your axles may not swap (length's varied), but the diff will. The one that came with my 55 was a 3.36 open setup. I replaced it with a 4.88 posi from a corvette.
I suspect you'll be fine for a while, but I'd take measurements while I was under the car just in case. I've witnessed one stand up alright to a 327 that was putting down a little over 500hp. It was fine for many months of straight abuse. However, when it did finally let go it was interesting to look at the pieces. I'd never seen an entire gear set turned to pieces no bigger than what you'd find in a cereal box (grin).