Protection of a 1.2V bus
Here's the device: -



On the basis of this table I'd say you will be fine operating it on a 1.2 volt supply - it's only going to take typically 1.5 mA on a 1.5 volt supply so with a 1.2 volt supply, current should be hardly worth bothering about.

Unfortunately the data sheet appears to have an omission - figure 1 does not appear to be included.


  Is there a better way to protect a power rail at this low of a
  voltage?


There probably is and it might be a crowbar protector. You have to consider the effects of distributed capacitance on your power rail and what sort of ESD event your board actually receives. You should be able to make a basic LTSpice model of both the event (human body model) and board capacitance and distributed inductance. Human body model usually falls into to groups: -



I can't tell you which to choose as typical for your ESD event, you have to decide that but, when you do you simulate the cap being charged to 4kV or 8kV (your research is needed here), do a simulation of this connecting to your distributed capacitance (seperated by PCB inductance) and see what peak voltage you get.

You are looking to either not have a voltage rise that is going to damage anything or, if this is not possible, you are looking for the rate of rise to be slow enough so that a crowbar circuit can begin to work (in conjunction with your TVS).

You are likely to have a 3V3 rail or greater so something that monitors the rail and kicks in above 2V to turn on a MOSFET (or SCR) to crowbar the supply is an option worth considering.