common emitter problem
No, the output impedance is not zero. To figure it out, try increasing or decreasing the value of the current source by some small increment, and then calculating the resulting change in output voltage. &Delta;V / &Delta;I gives you the effective impedance of the resistor+transistor circuit, which is also the output impedance, since the impedance of the current source itself is infinite.

You'll find that the resistor and transistor together act like a simple resistor that has the value R2 / &beta;. I'll leave it to you to derive this mathematically.