Hi Karyssa!
Thank you for visiting the Moms Panel!
The second week of January is a great time to visit Walt Disney World Resort! The average high/low temperatures are 72/50, with an average rainfall of 2.4 inches. So you certainly will not have to battle with the heat, but it is still warm enough to be enjoyable.
The crowd levels are also usually at their lowest from the second week of January until the first week of February (excluding Marathon weekend).
There are many things you daughter will enjoy. Head for Fantasyland in the Magic Kingdom park as a starting point. Also, check the website to review all the
attractions - they are all categorised as being suitable for different ages. You'll want to make a note of those that are "Fun for Everyone" and "Fun for LIttle Ones". As you enter each park, pick up a copy of the Times Guide which will give you details of all the character 'Meet & Greets' for that day.
If you have any other planning questions, please come back and ask me - I would be happy to help you plan your magical vacation!