Hi Jackelyn!
You can get more information on the various
Disney Dining Plans here. Just click on the link for the appropriate plan on the right side of that page.
The problem is you will not have enough children dining credits and adult dining credits to do what you are suggesting. The 2013 Quick Service Dining Plan consists of 2 Quick Service meals per person plus 1 Snack. The adult dining credits are pooled together and the children dining credits are pooled together, but since you only have one child (in the eyes of Disney based on age), you only have one child's worth of credits. However, you could ask if you can use an adult Quick Service dining credit to order off of the kid's menu. Officially you can't do that, but I think it never hurts to ask at Disney because of Disney's fabulous guest service. Just don't be surprised if you are told "no".
That said, Quick Service children meals are relatively inexpensive so you could always just pay for it out of pocket for your 10 year old if that helps to avoid fights! I know that is not ideal, but that might be the easy answer.
I'm sorry I don't have a better answer for you, but please write back with more questions!