Seconded. It is repeatedly implied in MoR that a noble child is, by default, a legitimate representative of their family, and anything that they do, or is done to them, is as if it was done by/to the family. For example, noble Slytherins get private chambers, even though they've done nothing to earn them within the context of the school's own regulations. Pretty much everything Draco does is considered to be a reflection on the House of Malfoy. It is considered natural for prepubescent children to know spells and rules of challenge designed for formal duels between noble houses.

In general, Rowling's universe assigns improbable values of agency and responsibility to children (socially speaking), and Eliezer only enhances this trend. Let's not forget that the Wizengamot doesn't blink an eyelid at sentencing a twelve-year old girl to die of slow torture for her crimes, or at a twelve-year old boy spontaneously giving away one of Britain's bigger fortunes to settle a blood debt. Death is an acceptable risk in exchange for having your child study at a wizarding school, with Hogwarts's no-deaths-for-fifty-years being seen as an amazing exception rather than a reasonable standard. Powerful magics are taught to children as soon as they are physically and mentally capable of casting them, with no reference to issues of maturity.