Ok, I've lost two fingernails before. In extremely rare cases, the nail will grow back perfectly fine but look different (ex: larger shaped) than the same nail on the opposite finger/toe.
You don't want to cover it with a bandaid unless it is bleading. The sooner it dries up, scabs over, and heals, the sooner a nail will replace it. Putting a bandaid on it at any other time will keep it moist. If it looks like it is getting infected or anything seems to be sticking to it (lint, etc) pour some hydrogen peroxide on it until it stops bubbling (you know what I mean) and let it air dry, then gently dab on some neosporin.
Losing a nail can be extremely painful sometimes because it feels like the nerves are exposed and just a small brush against it, or putting pressure on the pad of the finger, can cause make it hurt. You might notice your child is careful not to use the finger or touch anything with it and is whiny if he accidently bumps it.