No cure. Ever. Of course, you can complete the quest and save Timmy with both of you coming out unscathed.
First: no companions. This includes the dog. Do the quest solo.
Second: have a damn good one-shot kill weapon. Combat shotgun or plasma weapon.
Third: have all 4 perks of the weapon of choice to boost damage. This is important, because two of the molerats aren't one-shot kills.
Fourth: keep Jet (and at least 2 vials of addictol) on hand and/or have high agility. You'll need this for VATS.
Fifth: clean house. Move in quickly, then turn and back out. This will get the molerats out. VATS the weaker ones. If you can't one-shot kill them, reload the game.
The goal here is to take out the mole rats before they touch you. I would recommend a couple of run-throughs so you can memorize their pop-out pattern.
Then, give the vial to Timmy and you both are saved from the disease.
Enjoy!