Hatter would have made her a hat. If not a full size then one on a broach 

EDIT:
[img]https://s-media-cache-ak0.pinimg.com/736x/c4/09/92/c4099230776df74790c9c8aab615dd00--stick-pins-hat-boxes.jpg[/img]

Actually something simple like these.  They were meant to help ladies keep their hats on back in the day.  The teapot ones would be perfect because of his obsession