Simple, low precision, milliohmmeter
You won't get a lot of run time from the batteries.

1 A seems excessive.  If you really want to stick to that, I'd use bigger batteries, like D cells.

It seems your overall circuit strategy is to keep the base of Q2 at some adjustable voltage.  What you really want to do is keep the drop across R3,R4,R5 at a fixed voltage.  Feedback to regulate that directly would require wasting less drive current and get better accuracy.

It seems Q1, R2, and R9 is intended to be a crude shunt regulator, working against R1.  That uses a lot of current just to produce the adjustable voltage, and isn't all that good a regulator anyway.



I'd probably start with a better voltage reference, like a zener diode or a 3-pin regulator, then use a opamp to regulate the voltage across the current sense resistance.  The opamp would control a FET or a darlington to regulate the current.