LDO datasheet dont provide open loop gain plot
How to obtain open loop gain phase plot to compensate LDO, since it is not available in the datasheet. 


You don't. You just stick with the capacitor values given in the datasheet - 1 µF. 

Even if you could get a model of that control circuit (which will not by any meaningful degree be linear enough for a simple model that has a reasonably definable open loop gain phase plot that you're hoping for): 

What good would it do if you should find out you need, for example, 120 nF to be stable, you need to add 20% for tolerances, and then take the next bigger actually available capacity? You end up with a capacitor that would cost just as much as the 1 µF from the datasheet.