How deep does a quill stem need to be inserted?
I measured five quill stems that I have, three steel and two aluminum. The overall lengths vary from 5 1/2 to 6 1/4" (about 14 to 16 cm). The minimum insertion length was 2.5 to 3.0 inches (about 6.5 to 7.5 cm). There was not a consistant ratio of length to minimum insertion. It is possible that the insertion length increased on newer bikes due to safety/liability concerns. If you haven't got at least 2.5" (6.5cm) I would shop around for a longer quill or one that has an angled stem that will give you the height you need. An alternative is an adapter that inserts like a quilled stem but allows the use of threadless stems. The availability  and variety of lengths and angles on modern stems will give you more options.