My twins are just a couple of months older than yours. We took them at 10 months and they were great. At 20 months, it was tough. I think they would have been fine just a few months older, though.
The biggest issue we had was our sleeping arrangements--they're not used to sleeping in the same room so it was a big party every night.
Another thing was that when one would fall asleep in the stroller, the other would deliberately annoy him/her. If I had it to do over again, I wouldn't have brought the nice stroller; I would have gotten a couple of cheap ones that I could donate after the trip.
Finally, we stayed off site. We could have avoided so much hassle if we'd just stayed on Disney property. It's not such a big deal for other parks, but getting into the Magic Kingdom is a lot of work with two toddlers.
I think if you lower your expectations and take it slow, you should be fine. Also, Ariel's Grotto was the highlight of their trip.
Have fun!