Nooooooooo! I can offer nothing but sympathy, I'm afraid. I'm guessing that even if you get compensation, the dress can't be replaced. If your dry cleaner attaches tags, leave them on. That way when you go back with the damage, it's clear you haven't worn this since you picked it up.
Maybe Firecracker, Diane or one of our superstar stitchery artists can offer advice on fixing. I know that it's sometimes possible to get a re weave on woven fabrics; not sure on jersey. But sadly re weaving is a dying art, so few people actually do it properly; many just cut out a piece of fabric from a hem or non obvious place and patch the item (which can work if the hole isn't front and center) and call that 'reweaving.' I've had many moth holes in treasured items and am fortunate to have a friend who owns a high end dry cleaning business in DC, so he fixes me up -- even though I no longer live there.