Does a kid under Bar/Bas Mitzva have to tear Kriya when they go to the Kosel?
Mishnah Berurah, Orach Chaim 561:17. In fact, children might be forbidden to tear their clothes because of ba’al tashchit, the prohibition against wanton waste! See, for a related analysis, Minchat Chinuch 264:34* (Machon Yerushalayim edition, [Netanya, 5748]).
(Not that I'm commenting on whether it's a good idea to celebrate a bar/bat mitzva by an act of mourning; that's a different question but not one that can be answered in this forum.)
* 264:9 in the linked edition from HebrewBooks.org