No it is not recommended to give gatorade to children 2 years and under. This is because the sugar content is too high and may actually make diarrhea worse.
You can give your baby electrolyte solution such as pedialyte or Kao Lectrolyte once the baby is 6 months old. These are formulated to give your children the required amount of sugar and salt for rehydration.
Electrolyte solution are only supplements. Your still need to continue breastfeeding or formula feeding your baby while she has diarrhea . This will enable her get the nutrition and calories she needs.
Call the doctor if your baby, younger than 6 months has diarrhea. She may recommend an electrolyte solution as a supplement to breastfeeding or formula feeding. She may want you to bring the child in for checkup.
Content Sources
Are the Electrolytes in Gatorade Harmful to Children? Livestrong. http://www.livestrong.com/article/450807-are-the-electrolytes-in-gatorade-harmful-to-children/. Accessed May 30th, 2017