That type of constructions lends itself to a CNC router, in order to get the precision required, but a DIY approach isn't completely impossible.
Consider to create a graphic image using a vector editor such as Inkscape (free, multi-platform) or Illustrator or CorelDraw (both pay) to represent the holes of the join. Ensure that your graphic also includes a dot or cross-hair for each hole (see below). Cut out the printed version and attach to the work piece with suitable adhesive.
Wood is an organic material and it's going to be challenging to ensure the hole placement. The drill bit will wander from the desired location. Usually, one prepares for drilling metal by using a center punch, and rarely does so for drilling wood, but for this project, it would be a good idea to very carefully center punch the appropriate locations from the template.
Use a small diameter drill (1/8" or 3 mm) on the punched locations. This will serve as the guide for the subsequent drilling process. After your pilot holes are complete, use the final drill size to match your dowel pins. For best results, clamp the work piece to a scrap to prevent the drill bit from splintering on the exit. Using a forstner bit or a spade bit rather than a twist drill will reduce splintering as well.
It's unlikely that you'll have perfect results if the drilling is done using a hand drill. A drill press will provide the best chance to keep the holes parallel to each other and perpendicular to the face of the work.
If you have a makerspace nearby, they may have a CNC router or a laser cutter/engraver. I can envision using the laser cutter software to create the circular array, also called a polar array to create the shapes. Using high power would create the centering holes as well as the perimeter lines, reducing splintering and enabling precise drilling. Most hobby grade laser cutters will not cut through such thick material, but that's not required to accomplish the task.