I wouldn't think the crowds would be too bad then - but I have never been in January, or on a weekend...Make sure you use FP and you should be ok.
Not sure what your DD is in too - if she like HS Musical they have a parade/show that my kids loved - and then they get up on stage at the end and dance with the performers.
I hear the Aladdin show in DCA is awesome...
Maybe a character meal if there is a character she is really into...