I would underline with a nice sturdy cotton, rather than silk organza. I think I would probably sew some sew in polyester boning (Rigilene) to to the underlining (assuming it is also lined) - a couple of pieces front and back, along the grainline of the fabric. It won't support the skirt, but it will give it a nice structure.
I don't think I would want to add a waist stay for an eight year old for comfort, but if I did, I would do an elasticated one.
I would be tempted to look at an elasticated waist separate petticoat, instead of attaching the tulle, but do consider her waist definition, as
@Esme866 says.