Well, usually there is a different quest each day of the quest weekends.
But, they have decided to do something different this time. So, it's only the hat. I don't know when the rest of the costume will be out.
The only way to do the quest a second time is to use a mule (alternate character). If you have many of them, each one can do it once.
Other wise, the only other way is if the staff reset the quest.