I just celebrated my birthday at Disney last week, and it seemed to depend on the restaurant whether they'd do anything for a birthday. My sister mentioned to the hostess at San Angel Inn that it was my birthday and she was told to tell our waiter. Our waiter responded with, "We don't do anything for birthdays unless you call ahead and arrange it.........but Happy Birthday". Later, I was told that if I'd gone to Guest Services at the park and told them it was my birthday, I'd have gotten a button to wear and I would have gotten a free dessert.
We had dinner at Chef Mickey that night and I told them when we checked in that it was my birthday. They released our table to us early, put us in the front room, and during the celebration song they brought me a cupcake and Mickey came over to hug me.
I'd make arrangements ahead of time for a 4 year old, though, to avoid disappointment.