Bipolar junction transistor drawing more than 1 amp
You need resistors in the base leads of the transistors to limit base
  current, and thus collector/emitter current. Also, an NPN emitter
  follower can only pull things up - it can't pull things down. –  Peter
  Bennett


Thanks!

I fixed the problem by adding a 10K resistor to the base. I also rearranged the transistors so that Q2 is able to pull the output down; the collector of Q2 is connected to the output, and the emitter of Q2 is connected to GND.