What make a "Qualified Wizard"?

[Vivamus]

No: HPFGUIDX 118088


Sorry if this has already been addressed, but I'm trying to recall if there
is anything in canon about what makes a "qualified wizard".    The only
thing I can think of (other than age) is the OWLs.   If that's so, that
means Harry would no longer be under the underage decree, wouldn't it?

Does anyone have more canon information on this, perhaps from a JKR
interview?

Vivamus