Not necessarily. My 2nd grade daughter is one of the youngest in her class (a late July birthday). We have always heard from her teachers that she is one of the leaders in her class.
As a teacher, I have sometimes looked at a student's birthdate expecting to see that the student is the youngest (because of immature behaviors) only to find that the student is actually one of the oldest.
I think a lot of the students who are positive leaders have had positive role models, have had their leadership qualities acknowledged, and have been given opportunities to be leaders. They are confident in themselves and in their abilities. They know how to empathize and sympathize with others.
The negative leaders have had negative role models, feel a need to "prove" themselves, or are attention seeking. They haven't been taught leadership skills or had them pointed out to them. It is usually their charisma that fuels their leadership. They put themselves first and don't care how their actions affect others.
Many of the followers have "helicopter" parents who have done almost everything for their kids. They haven't let them take risks or fail. The kids don't have confidence in themselves or what they can do. Some of them are shy or deal with anxiety. They lack empathy and sympathy. They are behaviorally and emotionally more immature than their peers.
I think age is a very small part of leadership skills. As an adult, the best leader I deal with on a regular basis is almost young enough to be my daughter.