If possible, use this to your advantage here, and it can help you walk away with approximately half the experience needed for level two when you make it to the exit. Remember, if you have a fairly high agility, one of the best tactics to use versus melee enemies with only one attack is to first attack yourself and then use your remaining action points to run away from the creature.
There are approximately 20 rats in this cave, so consider fighting them using your knife rather than wasting the ammo in your pistol, unless you're running low on hit points.
Now that you've entered the world of Fallout, what is there to do? Start out by searching the nearby corpse for some advantageous early equipment, and equip it into your active slots.