Below is a section snipped from an infographic. Note especially the statements by the American and Canadian Dietetic Associations. Both explicitly mention that well-planned vegetarian diets (including strict vegetarian diets) are appropriate for individuals at any stage of life.
Caution: This does not mean that you can feed your kids kale and sunlight and expect them to be healthy. Unfortunately there are some exceptionally stupid people out there who have killed their kids by ignoring B12 recommendations, for example.