The ONLY reason the Commonwealth is able to regulate aviation is because Parliament DOES have a 'Treaty Power'. The Chicago Convention 1944 is effectively a 'Treaty' so the Federal Government uses it's 'foreign affairs power' as the font from which it is able to make laws to give effect to the Articles of the Convention.
The interstate trade and commerce power, the corporations power and the incidental power cover a lot of aviation safety regulatory ground, too, but not completely.