Right away, without a firm design, I think about starting with a 5/4" or 6/4" thick board for a bottom, a 3/4" board for a top, and 3 pegs as feet (instead of a pedestal) and a finial grab handle on the lid. You'll need a finial on the lid for a 5-6" diameter, she may not be able to grab that lid one-handed from the rim.
You could start with an even wider diameter base board, shaping a pleasing profile on the exterior diameter, to allow for a squarish/flattish interior. Consistent wall thickness outside to inside is not important.
First, shape the exteriors dish-like with decorative shoulder-tenon provisions to chuck-grab each piece from the finished exterior, like Raffan does, to be able to turn the insides second. While turning the outsides, drill deep holes for peg feet (short or long peg feet, your choice) and a sturdy finial lifting peg for the lid and glue them in (the feet and finial will need to be made first), then turn the base and lid interiors allowing the peg tenons to be visible as a finished detail. I think I'd want a good 3/16" of thickness left at the lid and base to assure durable glue joints at the feet and finial.
The lid can be fitted to the base as an interior recess fit to the base, or overlap the base, your choice. I would not seek the ego-boosting suction fit lid design- design the lid for easy one-handed on-off.
I suppose peg feet are important only if trying to maximize the volume of the base piece. Otherwise, a traditional/typical bowl foot design works too, skipping the three peg feet. A thicker base stock would allow for a taller bowl foot to create a pedistal appearance.
That's just a general, vague starting design that comes to my mind. I know Raffan has some similar lidded box/jewelry box design videos on utoob that you could scale up or down. Maybe use complimentary woods for base and lid. Have fun! (Huh, I should make one!)
