Welcome aboard, Stanley! You must be getting excited to set sail with Disney!
If you can find some space in your luggage to pack an empty foldable flat tote bag, you might want to do so. Disney Cruise Line does not provide all guests with a beach bag or tote. Guests who have sailed with Disney Cruise Line previously are considered part of the Castaway Club. Those returning Castaway Club guests do receive a special gift in their stateroom upon arrival, which usually includes a backpack. But, since I believe this is your family's first sailing with Disney, that will not be in your stateroom.
Disney Cruise Line's
Gifts and Amenities page offers quite a few gift options that are available for pre-purchase to be waiting in your stateroom. A couple of those packages include a backpack or bag, so you might take a look at those.
On the ship, I have seen bags for sale in the gift shops, so that's always another option. Most likely you'll go home with more than you brought, so it would be nice to have a bag to help carry it all back home!
I hope that helps as you continue with your planning for the cruise, Stanley. Please let me know if you have any further questions before you set sail!