You can get the Illusen Doll avatar if you complete one of Illusen's quests on Illusen Day (March 17th) which is TODAY.
Note: If you've already helped Jhudora, Illusen's arch-nemesis, on the same day you try to help Illusen, you will be unable to accept an Illusen quest until 12 hours has passed from the time you completed the Jhudora quest.