Hi, Shauna!
Generally speaking, Magic Kingdom tends to be more crowded on Saturdays, Mondays and Thursdays; this is in part due to the fact that most Guests arrive on a Saturday and want to start their Disney vacation off in this park. When planning my family's vacation itinerary, I always try to avoid visiting Magic Kingdom on Saturdays.
According to TouringPlans.com, for the week of January 13 when you plan to visit, the best days for touring Magic Kingdom with the lowest crowds are Monday, 1/13 and Wednesday, 1/15. The good news is that this entire week -- particularly Monday through Thursday -- is predicted to have extremely low crowd levels (2 and 3 out of 10)! All four Disney theme parks will become increasingly more crowded leading up to the Martin Luther King, Jr. long weekend, with Sunday, 1/19 and Monday, 1/20 predicted to be VERY crowded (a 9 out of 10).
I think your little princess would love dining with Disney royalty
inside Cinderella Castle!
Cinderella's Royal Table is a VERY popular dining experience, so I would recommend that you make a reservation as soon as you've decided which day you'll be visiting Magic Kingdom. Many young princesses enjoy dressing up in fancy attire for their meal with Cinderella and her royal friends. There will be plenty of chances to capture special moments, so be sure to bring your camera!
Please visit the Moms Panel again with any other questions as you continue to plan your trip.
Wishing you a magical vacation!