One of my colleagues (from a non-Australian background) referred to ‘Australian Day’. Why does that sound so wrong?
Mentally scouting through the world public holidays I know, overwhelmingly most of them are N, N day, Ns day, (the) N’s (birth)day, (the) Ns’ day. Offhand, I can’t think of any holiday which uses an adjective. If Bhutan has a public holiday for it, they would call it Happiness Day, and not Happy Day.