If there was ONE go to color, I'd say choose blue, but there really isn't only one color that works best. However, a mid-tone Blue is always a nice color, it looks good on everyone. It will stand out on light or dark backgrounds. If you end up converting any to black and white, it translates much better than red, which ends up a muddy middle grey.
Something formal and something casual is a good suggestion and will give you completely different looks.
White can be nice if you are completely solid technically, and know you won't overexpose and lose the details or end up with a dirty looking white. When it is all said and done, I would would worry less about the color and just avoid anything with words, tiny stripes, dominating plaids, etc. Simple solids will always work and won't draw attention away from the subject's face.
Give mom a bit of direction and have mom and kid pick some outfits together. (9 year olds should be given a bit of input. They will cooperate unless they feel like mom is making them wear something lame.) From the outfits they bring, you'll find something that works. Have fun! Make the little girl feel like a famous model and she will shine for you!