I would celebrate my child's birthday a month after, while in Disney. Especially since he missed his actual party because he was sick.
They make birthday's so special in Disney: They get a birthday pin, everywhere you go the CMs wish him a happy birthday, and he may get a cupcake at any of the sit down restaurants. If you go to a character meal, he may get a signed card from the characters at the meal.
My son was born at the beginning of September, right as school is beginning again so he doesn't tend to have birthday parties with his friends. Last year we took him Disney for his bday and he loved it.
We ordered a custom cake and it was amazing. There is a cake thread within the Restaurant section where people have posted some amazing cakes photos!! My son was so shocked when they delivered his cake right to our table at our sit down dinner !!!