Most likely that rat has diarrhea because somebody has fed something improper or something may have been wrong with the food. Kaytee has just had a recall on some of their pet diets, so you may want to check on the name of the food you have been feeding. http://www.petproductnews.com/headlines/2012/04/30/kaytee-recalls-batch-of-mouse-rat-and-hamster-food-due-to-salmonella.aspx
For now I suggest the Brat diet to help with the diarrhea: banana baby food, rice baby creal, apple sauce and toast. You can also feed a little canned pumpkin (not pie filling) which is a high fiber food that may help with the diarrhea. I would add some Plain Pedialyte for hydration.
If it does not start clearing or it seems to get worse a Rat savy Vet visit may be needed. You can locate rat Vets here: Put member in both blanks: http://www.rmca.org/Resources/vets.htm/
If the Rat has a parasite or a zoonotic issue it can be transfered to your daughter, so I would be cautious with her handling the rat. It would be wise to have a fecal check done on the Rat to rule out any of those issues. I would start the Brat diet for the rat and hopefully that will help resolve the issue. Joan