Developing software takes time. For now the driver and G-Code software is a quick and dirty work in progress. It's working, but still very early stage for testing. I created a small gear geometry using inkskape. Then I used the g-code-tool from inkscape to convert it in to code my machine can process. I turned the laser on, using protection glasses(!). A very bright yellow point was cutting the gear into a small piece of wood. So it's working pretty well.
But there is one thing that bothered me: The motors became very hot. So I had to reduce the current by adjusting the motor drivers. Then the motors had no power. I lost steps and the geometry was bad. Thank's to Paul Kocyla for the hint that my motors have a high inner resistance (27 Ohm). These motors have been produced for other purposes than mine. I replaced the motors with new ones with an inner resistance of 7 Ohms. Now the motors could break my fingers.
The next step will be to build a casing around the whole printer, because the laser is too strong to operate it without protection.