Character meals are fun, and the server will bring out a dessert with a candle at dessert time [free] ... it's a little weird that a character doesn't do it, but I guess then it would be Everybody's birthday every day! Since they don't make a huge deal out of birthdays (though the characters get excited when they see a birthday button), I wouldn't bother with the time suck or expense of a character meal unless it's the way your kiddo wants to spend the day.
We always take candles and a lighter and light up whatever treat the birthday kid is enjoying at an opportune moment and sing Happy Birthday.
On birthday morning in the hotel they wake up to balloons all over the bed, a couple of small presents, and Happy Birthday with a candle in a donut or whatever.
ETA I noticed you're staying at GCH. Make sure that her bday is listed on your reservation. They will give her a celebration folder with bday button, character photo, stationery, etc. -- basically a fancy version of what they give all the kids at check in.