Nothing in particular. Last time we went, my boys got a birthday card at each restaurant. At Chef Mickey’s, Pluto saw the card and got everyone in our seating area to sing to them. It was very special to my boys. At another restaurant, they each got a cupcake. I don’t expect anything, but would at least like to note it.
It's gotten to where it's best to just mention it when checking in at the restaurant. Disney has really cut back on the celebrations, simply due to the fact that almost everyone is celebrating SOMETHING at Disney nowadays. It's not like it used to be. You'll still get the cupcake at many restaurants, and a card signed by the characters at most character meals, but that's about it.
When making my ADR's a couple of weeks ago (I always call) they girl took a bit longer with out BoG reservation to make a note of my 1st grandchilds 1st birthday there. I noticed the same thing when I called in our reservation at AKL they noted it as well. If its just a birthday card fine, my daughter will be thrilled and she still has the cards she got from her birthdays at WDW.