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Yes you can plot the I-V characteristics of the Laser. You should replace the pulse source with the DC source and sweep the DC voltage. Put a resistor in series to DC source and the Laser. Put one resistor with very high resistance (1000k Ohm) in parallel to the Laser. Put one probe to the Pin of the laser (direction of going into the laser) to measure the current going through laser as a function of swept vdc source. Put another probe to the wire connecting resistor to measure the voltage across (which is equal to the voltage across Laser).
The schematic of the testing circuit is attached along.
Hope this answers your question.