Laser pointer circuit
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A possible correct version of the circuit.

Have another look and see if it's actually the circuit of Figure 1.

How it works:


R1 provides bias to Q1 which starts to turn on. D1 starts to light up.
When the D1 current through R2 reaches about \$ I = \frac {V}{R} = \frac {0.7}{39} = 18 \ \text {mA} \$ Q2's base will be forward biased, it will turn on and steal the bias away from Q1. (The turn-on point is 0.7 V.)
The circuit will stabilise at 18 mA.


This seems reasonable and will result in consistent operation across a range of battery voltage.