In shia islam we believe a girl needs to wear hijab at 9 year old because she becomes baaligh. However I think its more logical that she becomes baaligh when her menstruation starts, because there are ahadith that says this. Does this mean she becomes baaligh once her menstruation starts? Also most of the time a 9 year old has the body of child, changes happen usually around 12/13, so if becoming baaligh is when your body starts to change its more logical to me.

This is a disputed issue amongst scholars. Although the majority of the scholars say a girl becomes mukalaf at age 9, there are some scholars like Shaykh Ishaq Fayadh and Sayed Taqi Modaressi and some others who say she becomes mukalaf at 13.