I am posting at the direction of the in game support ticket people. I bought the backwards beanie and the startfleet knitted hat from the Q WW store. Opened the boxes and they did not appear in my clothing options. I logged off, closed the game, waited about 24 hours before relaunching and trying again. Still no items under headgear. Even bought another of each item, still nothing.
Fed Human toon.
Comments
https://www.arcgames.com/en/forums/startrekonline#/discussion/1268968/missing-toque-beanie-options
https://www.arcgames.com/en/forums/startrekonline#/discussion/comment/13754825
Seems there is a bug for certain races using the beanie, but I haven't tested that myself.