|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 an 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.