Please correct me if I've missed something here, but when clearing everything from my avatar (including turning off all the optional items from the 'base' tab) and wearing just the Timber Verevolf Tooth you can still see my avatars head, very clearly above the 'costume'. Looking at the design of the costume, it does look as though the fur across the shoulders is meant to rise up to disguise the head....
At this time there is no head toggle. You can use