Small and big drones all have different risks involved. Small drones have small parts that might be a choking hazard for small children.
On the other hand, bigger drones can cause bodily damage and death if not used properly. Some drones can fly at speed up to 50mph. As a parent or legal guardian, it is your responsibility to care for the safety and wellbeing of the minor piloting the drones and bystanders.
Some jurisdictions are putting age restrictions on drone pilots. Please check with your local authorities before giving a drone as a present to a minor.
If you understand the risks and are willing to assume them and also you are sure that the minor is a responsible pilot, we suggest you start them in the hobby with a small micro drone such as the Beta65 Pro 1S.
Read more on the topic in this article: Why is palm size micro drones the go to option for novice drone pilots?