The keto diet has been studied extensively in young children (some as young as three years old), elderly populations, and every age in between. There are even some cases of people (anecdotally from blogs) who have had their children on the keto diet since birth.
However, because of how the keto diet restricts carbs so significantly, it is best to monitor your health carefully as you are adapting to the diet. Some flu-like symptoms are normal at first, but if negative symptoms continue throughout the diet, then it is probably best to try something like a paleo diet or Mediterranean diet.