Hello MissHenn,
I know that royal caribbean has excelent children programs for all ages. The newer ship have things like mini golf, roller skating, ice skating, game rooms... all of which i am sure your 6 year old would enjoy. On my last royal caribbean cruise, the family that was also at our table had a 6 year old girl. She seemed to have the time of her life. There were activities planned for them throughout the day and mini-slumber parties at night.
Another cruise line to look into is Carnival. This cruise line is very family oriented. I don't know much about their childrens programs, but im sure they are just as good as royal. On the cruises I have been on, most of the people traveling on Carnival are families, (especially on a 4/5 day cruise)
I hope some of this helps!
Megan