|The following is based on promotional content and has not been confirmed by canon sources.|
The Vault Boy Bobblehead was made as a world object and a obvious reference to Fallout 3. It is available in the game when you enter the settlement of Wellsprings on Mayor Clayton's desk.
The Vault Boy Bobblehead is part of a line of bobblehead references found in the game Rage, along with a Blake Griffin and a Doom marine bobblehead. In game it serves no purpose except for a value of 150 dollars if sold.