I agree with Kuki in that your 6 year old will probably have a great time in the kids program on the ship. My 7 year old had an awesome time in the kids' program on the Disney Magic last year -- he never wanted to leave!
As for traveling with children younger than 6, I disagree. When we sailed on the Disney Magic last year we also took along our 16 month old son and our 5 month old daughter. We had the little ones with us the whole time except for a few hours a day when they went to the Flounders Reef nursery on board. We loved having our babies with us but those few hours a day away from them also made it a more enjoyable vacation for us.
We love spending time with our children and I think a family vacation should be just that: you spend time with your whole family, no matter what age your children may be. We tend to get so wrapped up in our day to day lives sometimes that we forget what it's like to just "spend time" with our kids and enjoy them for whom they are.
If a cruise line can provide quality childcare by caring providers in clean, child-safe areas, then I think there is no reason to leave our little ones at home. The Flounders Reef nursery on the Disney Magic was a clean, safe environment with many toys, and the caregivers were exceptional. I think my children benefitted from the time they were there.
As for what happened to Sheila and her family, I am shocked and hope that the matter is fully investigated.
Nevertheless, I hope you and your family enjoy your cruise together.