Hi Julia,
I believe that you are staying at
The Cabins at Disney's Fort Wilderness Resort, which is a wonderful place to stay. My family and I love the feeling of being at a campground with the convenience of our own cabin, complete with a full kitchen!
Right at Disney's Fort Wilderness Resort, you can visit the
Settlement Trading Post or the
Meadow Trading Post for a limited selection of groceries. You could also order groceries through the unofficial site gardengrocer.com before you arrive at Walt Disney World, and they will deliver groceries to your resort. I do not believe that I have seen birthday cakes at the Settlement Trading Post or the Meadow Trading Post. You can have cakes delivered from Garden Grocer.
Another great option for getting a birthday cake for your daughter is to call the Disney Cake Hotline at 407-827-2253. There you can speak with a cast member about customizing a cake for your daughter and having it delivered to you. When we celebrated my daughter's seventh birthday at Walt Disney World, we had a chocolate cake in the shape of Minnie Mouse's face delivered to our villa at Bay Lake Tower at Disney's Contemporary Resort. It was delicious and adorable. The unofficial site disneyfoodblog.com has a great article answering frequently asked questions about the Disney Cake Hotline. To find it, visit the site and search for "Cakes FAQ" and it should be one of the top links.
I hope that these thoughts are helpful for you, Julia. Have a wonderful time planning your trip, and please do not hesitate to ask if you have any further questions.