To answer your question, to get next day hair, you don't need to get a satin cap. If you can, put her hair in two to four braids for her to sleep on at night (to protect her hair and cut down on tangling). Do not wet her hair at this time if you are wanting her to wear her own curls in the morning. If her hair is still too short for that, it's fine for her to sleep in her curls loose until they are long enough to braid.

In the morning, undo her braids (if you've put them in, that is). Her curls will look smashed and fuzzy or even a bit stiff in the morning. This is totally fine. Wet your hands, put a little bit of the same combing conditioner on one hand and rub your hands together. Then smooth this over her hairline. Repeat, this time run your wet, conditioned hands over the ends of her curls. Repeat, but this time twirling and finger-combing any individual curls that got smashed and fuzzy while she slept. Wet your hands and add conditioner as needed, until her curls are damp and smoothed. Then leave her curls alone to dry. They should spring back to life when they dry.

Following this technique every morning, her hair should last 4 to 7 days between washings and combings.