Canada doesn't have specific legislation dealing with children's privacy, but by implication.... In PIPEDA there are, among other things, consent rules. Children, and certainly children under the age of 13, would not have the legal capacity to provide their consent. By virtue of certain activities they would engage in, the consent of a parent or a guardian would be required in order for them to legally engage there. So the parent, in that vein, steps in the shoes of the child.
Probably more robust than COPPA, we have in addition to the consent rules the full range of other requirements that an organization would still have to comply with—the security, the notice to the parent, the retention practices and the destruction of personal information, and the rights of access that would be afforded to the individual parent.
So you have a full complement of legal requirements and obligations that would still suffice, but you have fundamentally that consent provision that someone under the age of 13 wouldn't have legal capacity to provide.