This quest is hard, but it’s worth it in many ways.
First of all, find Vault 81. It’s a cool place, kind of like Vault City in Fallout 2. It’s still populated. After visiting the doctor, you’ll find two people arguing about a sick child. Find a secret passageway, and go in. There will be robots and special mole rats. The mole rats infect you with -10 max HP when bitten, so watch out. After you reach the end, you’ll meet a robot. Go to the robot, pick up the bobblehead inside, and then go back. Visit the doctor again, and then choose one of the following:
Benefits for saving the child
-Vault 81 condo
-Pick up almost everything
Benefits for keeping it
-Remove mole rat disease
If you do either, you get the robot as a companion, who’s also pretty good.
A way to do both at the same time is pretty dirty, but it works well. Say that you’re keeping the cure. Some companions will hate it, so when it says that, reload, and then tell your companion to wait outside of the elevator. Once you say that you’re keeping it, before you say “You’re right”, press the third person button, look away slightly, use the cure, and then look back and say “You’re right”. Now you have special things from Vault 81, and you don’t have a disease. Problem solved.