This project contains some experiments with Lego DUPLO and personal fabrication. Similar examples can be found at http://www.thingiverse.com/tag:duplo.
Dimensions and more information about Lego and Duplo bricks can be found at http://www.robertcailliau.eu/Lego/.
If you cut material you must think about the width of cuts, for instance laser cutters burn away some material. I expect this to be about 0.25mm, so I'd naturally get the required gap between parts.
Unfortunately I have not found a satisfying CAD software for 2D design, so I started with Inkscape.
You can use any stable material but plywood might be the best choice. 2mm, 3mm, 4mm.
Either you have access to a 3D-printer, 2D-Cutter etc. or you must order the parts at some service. I tried formulor.