Differential resistance for a zener
Like Mike says, 1mA is not really much for a zener. For low-voltage zener diodes zener voltage is often specified at currents as high as 50mA. The following graph is from the datasheet of a different diode, the MMSZ5225BT1G:  

  

Note that at \$V_Z\$ the curve isn't very steep yet, the derivative \$\dfrac{dI}{dV}\$ is low, which means that a small change in current (Y) results in a relative large change in voltage (X). For this diode the zener voltage is specified at 20mA, that's where the curve is much steeper (larger \$\dfrac{dI}{dV}\$), and the resistance at that current is "only" 29\$\Omega\$. This means that a 1mA difference will result in a 29mV voltage change. That's 1% of the rated voltage, and that's why I put the "only" between quotes. It's a typical value and it shows the limitations of a zener diode: you have to keep the current under control to have a good regulation.  

I've seen several low-current zeners, specified at 50\$\mu\$A, but none of them shows anything about differential resistance in the datasheet. Perhaps not really surprising, because the figures would probably look very bad.