Hi Chad!
How unfortunate! I recently went on a trip with my children, and found myself "hand-sanitizing" them every 5 minutes leading up to the trip :-)
But you know what? Even with all the precautions, My son STILL ended up getting sick at the end. But at least it was on the very last day of the trip (whew)...
You can postpone or defer as often as needed. In fact, that may be the way to go vs. cancelling altogether (with a $200 cancellation fee-ouch). Disney, I've found, has implemented a new policy for changes though. If a change in your reservation equates a change in the package price, Disney is now charging a $50 change fee, so be sure to ask before making even a date change.
Good luck! Here's wishing for a speedy recovery to your children and not a cancellation or change at all :-)