Only by doing several dummy bookings, and even then it could change from the time you start the process until you stop. Each booking will show you a variety of rooms available within your selected category, but not always the same ones (usually 6-10 rooms at a time).
DCL (as well as most cruise lines) doesn't release that information to the general public.
This only applies to the available cabins also. The ship can block out any number of cabins for maint reasons during a cruise and you'd never know which are occupied and which are getting some kind of rehab.
GET UP TO A $1000 SHIPBOARD CREDIT AND AN EXCLUSIVE GIFT!
If you make your Disney Cruise Line reservation with Dreams Unlimited Travel you’ll receive these incredible shipboard credits to spend on your cruise!