Hi Josette,
Don't worry, if you follow a few simple tips you should be able to get the dining reservations you require. Firstly all reservations can now be made 90 days in advance, I use the calculator at
www.pscalculator.net to work out exactly when I can call. As you arrive on September 27th the date you can call is June 29th. If you're staying at a Disney owned resort then you'll be able to make the first 10 days of your reservations on that date too. The dining number is 407-939-3463 and the lines open at 7am EST so make sure you call at EXACTLY 7am on September 27th. It may be worth doing a trial call the day before just to see how the system works as there are several steps to go through before you actually get to speak to a castmember. As you want Cinderella's Royal Table ask for this first, try and be flexible with your time, for example I once asked for 9am and was told no, so I asked for any time between 9 and 10am and they had a reservation at 9.05am which obviously I was very happy with. So be sure to give a block of time that you'd be happy with, also lunch at CRT seems to be less popular than breakfast so easier to book. As Chef Mickey's is also very popular ask for that reservation next and continue asking for reservations in order of popularity and again be as flexible as possible. Also have it noted on your dining reservations that it is your daughters Birthday!
Obviously it isn't guaranteed you'll get them but using those tips I've always managed to get every reservation I've wanted including Cinderella's Royal Table, Chef Mickey's and Le Cellier and at the times I wanted too.
Good luck and have a fantastic trip,
Jo