According to this guide, most essential oils should be either used when kids are above 2 years or above 6 years. If they are properly diluted, then it should be okay. For example, essential oils like eucalyptus, peppermint and rosemary should be avoided for kids below 10 years. http://www.learningabouteos.com/index.php/2014/02/07/essential-oils-and-children/
I started diffusing for my coming to 3 yr old since she was three months old. Right now am using like half a drop to one drop for application under her feet.