Hello Lizanne,
Thank you for your question to the Disney Parks Moms Panel. Celebrating at The Happiest Place on Earth is going to be a memorable occasion and I'm so excited for you all.
The Disneyland Park differs a little from the Walt Disney World Resort's Magic Kingdom in that it does not have an actual room in Sleeping Beauty's Castle like in Cinderella's Castle. However, the Disneyland Resort does have specialty suites available at the Disneyland Hotel that are themed that you may like for the occasion.
You may have heard about the Dream Suite above the Pirates of the Caribbean attraction. However this pixie-dusted room is only offered through promotions or magical giveaways and is not an option for reservations; currently there are no promotions at this time.
The standard room at each Disneyland Resort Hotel would hold a maximum of 5 Guests, there are Suites though that would accommodate the 6 Guests in your party. I would recommend you call a Disneyland Reservation Specialist at (714) 520-5060. You could also ask them about the special Ambassador Suite at the Disneyland Hotel as this one accommodates 6 Guests.
Celebrating birthdays with the mouse is always magical! Be sure to stop by Guest Services at either of the Disneyland Resort Parks and tell them you are celebrating your daughters birthday. The Cast Member will give her a free "It's My Birthday" button for her to wear; she will be sure to get birthday wishes and smiles all day.
I hope this helps and that you have a pixie-dusted visit. If you have any more questions, please visit me here at the Disney Parks Moms Panel and let me know how I can help you plan your magical vacation.
Have a Zip-a-dee-doo-dah Day!!
~Lynette