The hole will close, whether or not it will "vanish" is a separate matter. That young, they usually do. In a year or two, however, the holes usually become permanent EVEN though they are healed/closed there will still be a dot or indentation from the original hole.
I *HIGHLY* recommend Slave to the Needle in Phinney or 45th near the UW just west of I5. Best shop in the Puget Sound... and their piercers are licensed and certified... that's ALL that they do. Going to a good tattoo / piercing studio is quite a bit more expensive than the mall (typically around $30 + cost of jewelry.., not sure about current pricing) but you really get what you pay for.
http://www.slavetotheneedle.com/
http://www.slavetotheneedle.com/piercing/policies.asp ((On anyone under 12 they will *only* do earlobes))
They don't use a gun, but aseptic piercing with needles. It hurts a great deal LESS with a needle, placement is perfect, and the holes heal better and faster since there is no "smashing" of the other tissue. Clamp. Needle. Jewelry. Unclamp. Finis.