Timmy is saving up for a sparkling new Red Racer tricycle, just like the one Betty has, but won't let him play on. As mommy told him: "if life gives you lemons, make lemonade!" Timmy took her advice literally. Then he'll show Betty; perhaps then she won't make him cry this time.
Timmy came with his parents to Vault 112 and has been in a tranquility lounger for more than 200 years. As Braun said, if the tranquility loungers were to be disabled, he and other residents would lose their "life support," and die almost instantly.
Bill Foster describes him as what he called a "momma's boy" back in his day.
Timmy's vitals (especially his heart rate) are concordant with a child's. However, when you look in the lounger assigned to him, he uses the same adult male model used by the other male Vault 112 residents.
As is the case with every child in Fallout 3, Timmy cannot die on-screen at any time. If the Failsafe is activated, he will not be present anywhere in the simulation. However, examination of his vital signs after leaving the simulation will verify that he died with the other residents.
The following is based on Fallout 3 cut content and has not been confirmed by canon sources.
Originally, Timmy was supposed to be killed, unamusing Betty, who asked the Lone Wanderer to make him miserable and would revive him. Since children cannot be killed, this piece of dialogue is unused.
End of information based on Fallout 3 cut content.