I've made a bat costume a couple of times. It's easy and fun.
I'd go with a solid colored matching set of leggings and long-sleeved t. Can be any color (Maybe your dd wants to be a purple bat.) You can then make an easy furry tummy/back with a 1 yd ish piece of fake fur (get creative with colors here, too). Cut a hole in the middle for her head, put it on, and trim out a belly/back shape.
For wings, I like the play silk idea, trimmed in a bat wing shape and pinned to the top or sewn to the underside of the sleeves. I think Dharma Trading has black silks.
Then I'd take a headband and attach left over bits of the fake fur to make ears.