7 years old?
Actually more in keeping with the beginning age of students as a whole
I always wondered were all wizarding children Home Schooled to age 11 in the HP world because that's a subject they don't exactly touch on in the books or movies

The school is a place where the bonds of friendship are formed so it is important
What if some do actually go away to the big wizarding schools 

In the wizarding world, there are eleven[1] schools for teaching young witches and wizards magic. 
The three largest and most-well known schools in Europe are Hogwarts School of Witchcraft and Wizardry, located in Scotland, Beauxbatons Academy of Magic, located in France, and Durmstrang Institute, located in northern Scandinavia. These three schools are connected via a competition known as the Triwizard Tournament, with the winning school getting a trophy to take back home.  Outside of Europe, known general magic schools include Mahoutokoro in Japan, and a Brazilian wizarding school of unknown name.
A Salem Witches' Institute is mentioned in Harry Potter and the Goblet of Fire. However, it is unclear if this is meant to be a wizarding school, or rather some other sort of wizarding institution, such as an American wizarding counterpart to the real-world Women's Institutes.
But these would only be five of them listed and the others are not so where they are and their names left for speculation
But it would be feasible that some would leave to go there because of various reasons Such as parents or lack of being able to gain a position as an apprenticeship