Hi Melissa,
How wonderful to take your stepdaughter to Walt Disney World for her first trip and to celebrate her 10th birthday! There are so many fabulous ways to celebrate a birthday at Walt Disney World.
First, I suggest that you pick up a "Happy Birthday" button for your stepdaughter at Guest Relations at any of the theme parks. By wearing this button, she will hear guests and cast members alike wishing her a happy birthday all day long. Also, you never know when a little extra pixie dust may be sprinkled on her day. My daughter received a huge cupcake at The Plaza Restaurant while wearing a birthday button! This kind of magical moment is not guaranteed, but is certainly wonderful if it does happen. At her age, you also might consider a visit to Senses Spa at either Disney's Grand Floridian Resort & Spa or Disney's Saratoga Springs Resort & Spa. Each of these has a Kids Menu with services such as manicures and pedicures that she might enjoy.
As to coming with a baby, I traveled to Walt Disney World with my daughter when she was very young, and it was a lot of fun. It will be hot at the end of June, so do travel with a sunhat and sunscreen for your baby. I also always tried to get my daughter back to the resort for at least one nap a day, and tried to stay on her schedule as much as I could. This made for a much happier baby, and thus, a much happier me! Also, take advantage of the
Baby Care Centers at the theme parks. These offer a cool and relaxing place to feed and change your baby, and just to relax for a while.
I hope that these thoughts are helpful for you, Melissa. Have a great time planning your trip, and please do not hesitate to ask if you have any further questions.