Hello Jamie! Welcome to the Disney Parks Moms Panel.
Celebrating your niece's birthday with Advanced Dining Reservations for
Fairytale Dining at Cinderella's Royal Table sounds like an Endlessly Magical Experience.
Normally, I would suggest to Guests that they order a customized cake from the various cake options available from the
Birthday Celebration offerings and calling (507)827-2253. However, based on your response, it would appear you have already looked into that and besides, customized cakes are not available for delivery to Magic Kingdom Restaurants.
Most dining locations have a chocolate or vanilla 6" cakes for spur-of-the-moment celebrations, but if you are looking for a customized cake to celebrate your niece's birthday, I would recommend that you bring one to Magic Kingdom, yourself. I have checked with Guest Services and birthday cakes may be brought into the parks for celebrations. I do recommend that you inform Cinderella's Royal Table a couple of days in advance of your reservation informing them of your intentions at (407)934-2927 in order to ensure they have room to store your cake before it is needed.
If you are looking for an additional experience to add to your niece's magical experience, you may want to consider Bibbidi Bobbidi Boutique - Magic Kingdom. Located beside Cinderella's Royal Table, Bibbidi Bobbidi Boutique - Magic Kingdom
provides royal makeovers to children ages 3-12 by Fairy Godmothers-in-training and head-to-toe pampering.
Have a Magical Celebration!