My Electrologist does both laser and thermolysis. I started there within about a month of consulting a therapist. Soon after I started, I asked about having laser done. Her response was that, the time line for laser is actually longer than electrolysis. This is because of the down time between laser sessions (about a month) versus the recovery time from an electrolysis session (not much more than a few days) mean that more hours of electrolysis is possible in a month than with laser treatment. To top it off, only the electrolysis removes hair permanently. The net is that the laser takes longer and isn't permanent, while the electrolysis is both permanent, and has a shorter cycle time, so can be accomplished sooner.
One final item, as you have hair removed, what appears to be new ones will spring up, especially if you are pre-HRT. Don't be alarmed by these hairs, they're growth cycle will be accelerated by the death of other hair follicles which frees up DHT that was causing the now zapped hairs to grow. These will be zapped as well, and before you realize it, you'll be hair free. I heartily recommend skipping laser and going straight to electrolysis as soon as you accept you're transitioning. However, I must acknowledge that each of us will have different results, and my timeline and you're may not be the same.
-Alana