These tips aren't birthday specific but can be done to make your trip more magical.
Are you going to Epcot ? If you are, go to the Japan Pavillion and their store, there is a spot call Pick a Pearl. They have an open water tank full of oysters and for about $15 you can pick out your own oyster. They will fish it out for you, open the oyster and find it's pearl. They will measure the pearl for you and then have a fun little ceremony. Both myself and my daughter got pearls and she loved it. She wanted to wear it all day. In fact, when we go backone day, I would like to make it a tradition. We both get pearls. They have settings you can put your pearl in, but I got mine off of Ebay. Just look for pick a pearl carriage. I would send a link but Ebay is having trouble right now.
Also in Epcot is Agent P's special agent adventure. This is where the kids pretend they are going on a secret mission around the world to catch the bad guy from the show, Phineas and Ferb. At the beginning of their mission, they will get a special secret agent phone. With this phone they will make special little things happen in each pavillion, like making water come down a waterfall or beer steins sing and dance or a bonsai tree come back to life. My nephew did this and he said it was his favorite part of the trip. He couldn't get enough of it.
When you go to the Magic Kingdom, go to the show Mickey's Philharmagic. This is a fun 3D show where Donald gets to meet various Disney characters. In one scene, he meets Ariel and she opens up one of her treasure boxes full of jewelry and throws them at the audience. Again, since it is 3D it will look like you can just reach out and grab the gems. Well that is when you reach into your pocket and pull out a faux gemstone and give it to your DD telling her that you caught one. My husband and I did this to our DD and she was amazed. She couldn't believe that mommy and daddy caught a gem. She even keeps her gems in her jewelry box at home. We got the gems at Michael's craft store. They have some in the home decor section by vases and bowls. We bought the uhhhh diamond and ruby.
If you go on the railroad in the magic kingdom, try to be on the last car. The conductor might let your DD yell "All Aboard" on the megaphone.
I don't know if this is still true, but if you go on the Riverboat in Magic Kingdom, ask you you can go in the Pilot house. This way your DD can meet the riverboat captain.
If you go to the fire house station on main street, ask if your DD can be a fireman for the day. I think they will give her a little certificate.
If you want your daughter to pull the sword from the stone, there is a little trick to it from what I hear. It doesn't happen for everyone. Try to make sure she is the last and the littlest one of your group to try. It also helps if the adults in the group make a big show of how they will surely pull the sword from the stone because they are the biggest and the strongest. Again, make sure she is the last and hopefully she will pull the sword from the stone.
If you are able to watch the fireworks at MAgic Kingdom, look up for a line that connects from the Castle to Tomorrowland Terrace. Try to stand underneath the line and you will see Tinkerbell fly right over you.
At Hollywood studios, go to the Muppet show. At the entrance there will be a sign saying "The key is under the mat." If you look under the mat you will indeed find a key.
Also at Hollywood studios is the Indiana Jones show. Outside of the show, is a well with a rope. If you pull on the rope, you will ear someone yelling from down in the well.
Is your daughter a Star Wars fan too ? If so then try to get to Hollywood studios really early and sign her up for the Jedi Training Academy. Here she will be onstage and receive a robe and lightsaber. A Jedi master will teach all of the kids some lighsaber skills when all of the sudden Darth Vader will show up and try to lure the kids over to the dark side. Each child wil get a chance to fight Darth Vader and when it is all done, they will be receive a certificate. My nephew also did this and loved it.
Disney truly is a magical place and I know your DD will hae a great birthday.