I've noticed it twice. The day after she offered a hat to my mayor character she offered one to my second character. Both happened to have a bad-luck day though and they were all celebration hats.
Katrina charges 10,000 for each hat. After you have gotten one or cataloged it from someone else, they are re-orderable for a whole lot less. I don't remember the amount and I don't have the game on right now, but maybe around the 1,000 bells or less.
I don't know if it is just luck when she offerers the hats, but I had gone to her shop to get my daily fourtune for 20 straight days and she sold me the Celebration hat. Then 20 more days of daily fourtunes and then she offered the Tingle Hood. This happened in both of my towns. Of course, you can't have the lucky items on already when she reads your fourtune, otherwise she won't offer the special hats. And this is for a single character, unlike the 20 readings in her tent to unlock the Main Street Shop.
Good luck everyone.
It really is plain lucky, she offers you hat when you're unlucky, so just run to her shop when you find yourself tripping. Got mine hat on the 3rd day I've finished her pwp.