P.M.
My husb loses at least one of his big toenails every year after his big annual trek into the wilderness. Repeated pressure on the toes during long descents takes a toll. We just keep the nails trimmed as much as possible during the gradual release so they don't snag on socks and pull off painfully. Takes them a year to come back to normal, and then he goes off on another hike…
Your daughter's nail will probably be fine, eventually, but getting rid of the damaged part is hardest. Keep snaggy edges trimmed as short as possible. I agree that covering it would probably help – I wonder if she'd help you pick out some "special" band aids?