I got a cake last August for my mom (or at least a chocolate slipper at 1900 Park Fare). You have to call the ‘cake hotline’ to order. But I think you can just tell the person at the podium it’s someone’s b-day and you’ll can order the mini cake right there. (The phone line is for bigger cakes and special ones).
I’ll also second the Disney Florist. I used them to get my mom balloons and then my sister did that as well. Both times they were great to work with.