There is something that nobody has mentioned yet, that we have discussed before in other threads and I will take this opportunity to add it to this discussion...
You work hard for your child, you give most of your energy to them to help keep them safe and integrated and as happy as you can get them. But please don't forget, this is YOUR vacation, too. You need a break, some time to relax and refresh, time to explore and break out of your role as caretaker for a bit. You NEED a vacation. Your child NEEDS you to have a vacation. You should take advantage of any opportunity to get a break and take it easy on yourself, for yourself. That isn't selfish, that isn't neglectful, your child will survive if you get a brief respite.
The kids clubs will take special needs kids in most circumstances, and my experience has been mostly good with those. I know that the one at BWV was staffed by people who used to be special ed teachers on the night that we took our kids there. Also, the Fairy Godmothers child care service, and others as well, do care for special needs kids. Several of us on this board have used their service and found it to be excellent.
After a few hours, your autistic child may have had enough, but you may want to go on... they may very well be much happier in a kids club, or in the room with a nice, experienced sitter, than they would be to be out for a full day and evening of fun with you. And you pay a lot of money to go there for a FAMILY vacation, not just for your children but for you, too. There is plenty to do for adults at WDW, there are opportunities for respite there... consider taking advantage of them for a few hours.
I also did a respite trip on my own this February - actually with several others from the DIS who were doing the same thing. We pretended we were being wild and crazy, but we were, in fact, several women who really needed a break from our caretaking roles for a few days. My trip report is on the old Trip Report Board somewhere... It was a wonderful break. You should think about that! It is an opportunity.