My daughter fell and landed on her face. now her tooth is black and i am worried if this is maybe permanent or will it be white again. shes 4 years ?

Likely dead: The root of the tooth likely broke off with the trauma and now it will sit as a space holder until the adult tooth comes up. You can check with her dentist on this but don't be surprised if there is nothing they can do to resurrect it now.

Trauma: Yes, the discoloration is probably permanent and indicates damage to the internal structures of the tooth. There may also be damage to surrounding bone and/or underlying permanent tooth. Your child should have been under the care of a Dentist, preferably a Pediatric Dental Specialist, since her 1st birthday. Dentist will therefore have baseline for comparison. See your daughter's dentist ASAP.

No its dead: The blood flow was interrupted to the tooth and the tissue within the tooth has bled into the grain of the tooth and caused the discoloration. Most times the nerve has died and an infection is starting in the bone under the gums. You may find a small "pimple" up high in the gums above the tooth that will express pus when pressed. this tooth needs to be removed. good news, new one in 2yrs.