Hi Rebecca!
Wow, lucky duck! I love Cinderella's Royal Table and an early morning reservation is double wow. It is one of my daughters favorite character breakfasts.
I spoke to a cast member and was told that stroller rental at the Magic Kingdom opens at park opening. So if there are extra magic hours that morning, then they will open for extra magic hours.
However, here is my unofficial answer. I know I have seen the stroller rental office open prior to park opening. So my advice would be to take a look when you arrive for your breakfast. If it is not opened yet, you can always send a member of your party 15 minutes before park opening to rent the stroller, so your whole party does not have to walk back to the park entrance.
If you are looking for peace of mind and definitely want the stroller with you, there are
several private companies in the area that offer stroller rentals.
Enjoy your breakfast with the Disney princesses and have a magical vacation!
Tania