For the experiment, can one electrode be connected to the LabJack's ground?
You are sure that the effective impedance between the two electrode is such that it only takes +-2mV for +-1mA between electrodes?
According to the LabJack
data sheet, the DAC is 0 to 5V, with 10bits of resolution (1024 steps). You need 2000 steps, so I recommend using a digital output to switch a small DPDT relay to reverse the electrodes at the center of the range, so you will sweep the DAC twice, once with +- polarity at the electrodes, and a second time using the relay to reverse the two electrodes.
If the impedance between the electrodes is as low as you say, you can convert the voltage from the DAC to a current just by using a single resistor. The value would be ((5*1000)/1024)/0.001 = 4883Ω.
You will have to write a VB program (using the LabJack supplied library) to step the voltage at the DAC output from 4.883V to 0V (1000 steps), flip the relay, and then step the voltage from 0V to 4.883V (1000 more steps). At each point, you will use one of the ADC channels to record the voltage across the electrodes. Since the input range of the 12bit ADC is 0 to 2.4V, you will need to use an instrumentation amplifier with a gain of about 1000 between the electrodes and the input of the ADC.