See http://doc.trolltech.com/latest/qscriptengine.html#newQObject The JSC C API's JSClassDefinition and friends can be used to implement this feature.
There should also be corresponding methods QScriptValue::isQObject() and QScriptValue::toQObject().
This related API should also be implemented: http://doc.trolltech.com/latest/qscriptengine.html#signalHandlerException
I've started documenting Qt's existing QObject binding here: https://trac.webkit.org/wiki/QtScript
Porting QtScript API over JSC C API will not be continued.