Hello Leah - nice to hear from you again! I made a couple calls yesterday to get the latest and greatest info on how this can be arranged. It seems like this will end up being a two step process. First, you'll need to contact
Disney Florist and let them know exactly what you are looking for. They do have autograph books and pens in stock (not sure if they specifically have a Kooky Pen) but they no longer carry the birthday hats. However, you'll be able to call Disney Merchandise Department (407-363-6200 or wdw.mail.order@disneyworld.com) to order the hat and any additional items you'd want for the basket and have it shipped to the Disney Florist.
Depending on what the above will cost, you also have the option (and this is what I would probably do) is order everything from Disney Merchandise Department in advance and have it shipped to your home before the trip. You can then bring a nice gift back and arrange it in the room yourself. (Note: I also thought of having them deliver to your resort but Disney Merchandise told me they will not ship to a Disney resort.)
Also, while researching, I did notice there are two types of birthday hats - one is with the candles on top and the other are birthday ears. You can find a detailed list of birthday products
here.
I hope this helps. Please let us know if you have follow up questions. Diane :)