MADE IT!!!! What it does is subtract 100mV(1mA x 100Ω = 100mV) from the output voltage of the regulator.And feeds it into the other side of the resistor.So that the current flowing through the resistor is always 1mA.
The opamp used in the real circuit will be lm358.
In the simulation it can work below even 500mV.
I will build it using lm358 and test it out, i think it will work in lower than 1V.
Here is the circuit (image)↓↓↓↓