Many years ago when I lived in the tropics, I caught a nasty tropical bacteria under both of my big toenails. They both turned black, fell off and happily, they both grew back perfectly fine.
Although my toenail demise was not a result of an accident, it's all the same: toenail turns black, falls off and grows back (perfectly normal).
Fourteen years later, and this is still a much loved story by the people who were around from those days. It's funny what people remember, especially since we spent so much time partying on the beach back then.

Good luck to you and your toe.