I would suggest that you get her seen by your Pediatrician
as there was a nose bleed.
Usually after head injury
if there is ear/nose bleed it indicates fracture
of the skull bones. How ever nose bleed can happen in injury to nasal structures also.
Loss of consciousness
, forceful vomiting, seizures all are danger signs after head injury.
Since after fall from stairs, chances of major injury are there, its better that you have your daughter seen by a doctor.
Hope my answer helps you.
Wish your daughter good health.