Hello Amanda! Welcome to the Disney Parks Moms Panel.
Your little one is in for an Endlessly Magical Makeover during her appointment at
Bibbidi Bobbidi Boutique at Disney Springs.
The best use of your day at Magic Kingdom would be to try and book Reservations for the
Bibbidi Bobbidi Boutique location in Magic Kingdom which would cut down the need to arrange multiple trips on
Complimentary Resort Transportation in order to get to both Disney Springs and Magic Kingdom (and possibly back again).
Reservations are hard to obtain, but cancelations are frequent and worth it in your particular situation, even if you get a different time for that date.
Aside from that, waiting for your 10:45am reservation will dramatically cut into your day at Magic Kingdom. If
Extra Magic Hours are offered that morning at Magic Kingdom and you have your own transportation, I would consider an early visit a worthwhile experience. However, if Magic Kingdom opens at 9:00am and you are taking Complimentary Resort transportation to and from Disney Springs, you can only safely give yourself about 30 minutes in Magic Kingdom before you will need to begin your travels to Disney Springs.
I wouldn't rush the experience with my family. Enjoy a leisurely morning pace, take the Sassagoula Boat from Disney's Port Orleans Resort - Riverside, experience your Magical Makeover and then make your way to Magic Kingdom.
Have a Magical Visit!
~Todd