If you're there to celebrate her birthday then go ahead and celebrate! Get her a free birthday button and if you go out for a special meal go ahead and tell them you're celebrating her birthday. There's no reason not to do birthday things when it's a birthday trip, even though it's not her actual birthday.
As far as costumes, there are all kinds of little girls in their princess costumes and I would imagine this time of year you might see lots of other types of costumes too. You didn't say how old your DD is but there is an age limit for costumes. I believe you have to be under 10 (?) to wear a costume to the parks - except for the ToT party. I will say my personal opinion on costumes though. It is really cute to see the little princesses walking around in their little dresses but to me it looks so uncomfortable for a full day of touring the parks. Just imagine wearing formal wear to DLR all day. So just keep that in mind that some costumes might not be that comfy to be in all day, especially if the weather heats up.
Hope you have a great trip!