The last time I was in Disney I recall a birthday cake being delivered while we were dining at 1900 Park Fare. The cake was absolutely beautiful; Ariel themed. I asked one of the CMs about it and she said you could have this ordered by calling 1-800-WDW-DINE or you could order it while on property. She did mention that the cakes can get quite pricey. If I remember correctly she said that you should have the cake ordered at least 48 hours in advance.
Good Luck
