Current source design
What you have there is a circuit that, when you increase the current through R1, the current through R2 will increase. 

However, that's the only thing that can be said about it for certain. The actual ratio of R2 to R1 current is poorly controlled. As you say, it depends on the detail of the diode and transistor base-emitter conduction.

It's easy enough to arrive at a current through R1 to give any R2 current, if you make assumptions about D1 and Q1 parameters, and the temperature. It will be dependent on which model the simulator uses for the transistor. Be aware that this mode is almost never used, well, certainly never trusted in this region, so the models may well be quite inaccurate, as they don't need to be accurate, as nobody would trust them here anyway. If you give an answer based on your simulator, make sure you quote the transistor model, and its parameters, in your answer.

You might well, for the sake of your answer, assume the diode conduction curves for D1 and Q1 are identical if you like, as long as you state the assumption.

To make a proper (robust with temperature, and various device types) current source, place a resistor in series with the diode, and a resistor in series with Q1 emitter. Aim to drop around one volt at the design output current. This will be sufficient to swamp the differences in diode voltage for most 'biassing' purposes, though a precision current source it still isn't.

For 100uA output, put 10k in Q1 emitter. Now you can choose the D1 series resistor to scale the output current if you like. A 100k resistor would result in an output current of 10x I(R1), a 1k resistor of 0.1xI(R1).