According to AnimalJamCentral.com, there is currently no code to obtain a headdress; however, one way to get the item is to trade with another player who already has the headdress. A second option is to visit the Animal Jam Store on a Monday when rare items are on sale.
After logging into Animal Jam, head to Jamaa Township, where many players go to trade. Once there, type into the chat bar to ask if any players have a headdress available for trade and negotiate with the other player. Be prepared to trade an item of the same or similar value.