Disclaimer: I am owned by two felines, Luna and Minerva.
First, I'd never travel with them (again). We moved from Detroit to Phoenix in May and it was NOT FUN for either the humans or the cats. We drove with them in a good-sized cage, and they were good girls, but they were also pretty stressed. And why would I take them to WDW, when we're not in our room most of the time - and when we are, we're dead tired. Nope, we leave them home w/2 boxes, lots o' food & water, and a trusted friend to check on them if we're gone longer than 5-6 days - I'm sure they're much happier.
Second, I'd never stay at a pet-friendly
DVC resort. While the smells/stains are an issue ( and I'd like to hear from anyone who's darling dog or cat has
never peed, pooped, puked or coughed up a hairball in the wrong place ), noise and behaviour would be my biggest concern. All it takes is one barking hound - or one yowling cat - to disturb a lot of people; and if they start setting each other off - well, the "Twilight Bark" isn't so great when you've had a long day....
Finally, if it came to an owner vote (yeah, right), I'd vote no. Pet-friendly places simply have more wear.and.tear, and cost more to keep up (IMHO, but there's a reason apartments and hotels have pet fees and pet deposits). I've read how some folks around here get upset (and justifiably so) when they check in and smell smoke, or find hair in the tub, or moldy food - think how you would feel if you checked in to your DVC room and found a present from Rover or Fluffy....