Again, I doubt the dog would wet it as much as you think... it is really really hard to soak a down quilt. I would be more concerned about the dirt/mud, myself. You could easily order some Goretex and make a removable additional shell for the quilt. I have one that I made to add to the kit while tarping on the ground in rainy, humid or windy conditions. That would also help as protection against dog nails, since the two ply, lighter weight Goretex from OWF (outdoor wilderness fabrics) is still pretty tough stuff. This would allow you to remove the Goretex and air out the quilt, maintaining the loft of the down without sacrificing the protection.

A cheaper way to do it - get a DriDucks poncho, about 12-15 bucks, and you have a double use item - a rain poncho AND a cover for the quilt that is more breathable than anything else you'll find. The only downfall is that DriDucks are fragile, but this will allow you to keep the water off the quilt, keep the dog claws at bay, keep dirt off the quilt... and be lighter than Goretex, tho less permanent a solution.

DWR means that regular nylon has been lightly treated with something to make it water resistant, not waterproof. A waterproof fabric will be given a more thorough treatment - many, like Goretex, are much heavier as a result. Polyurethane coatings are nonbreathable and probably the most waterproof of all - also heaviest. Fabrics like Epic, Event and Goretex will be somewhat breathable and waterproof (or water resistant - I don't think Event is really all that waterproof, but it's more so than DWR).

Technically, all fabrics are only waterproof to a certain point - for general camping purposes, some are waterproof enough.

Have you tried searching for more info? The search function sort of works. Another place for info might be Backpackinglight.com - they have articles on various fabrics in outdoor applications. Unfortunately you have to pay to get them, but they are a good source for technical info on a lot of backpacking gear. It might be worth a year subscription to sign up, if you are researching geeky details about gear.