Hoogerland National Railways has a particularly useful site with enough information and detailed dimensions to really explore this further. Woodat is another source for ideas and plans.

Take measurements from other railcars to get the proportions balanced. Magnets need to be set at the proper height (centered at ½" from wheel base) and oriented correctly too. More information can be found at these two sites,
pw1.netcom.com/~thoog/hnr/hnr.html
www.woodat.com

I ‘child tested’ the wheels using a glued 1/8" birch dowel axle. Within a few minutes of casual twisting the dowel completely disintegrated and snapped in the middle. Using a carbon fiber graphite shaft and CA glue held up better, but the glue set up so quickly it was difficult to get the wheel balanced on the axle to prevent wobble.

The wheel can be drilled to accept a larger 3/16" hard wood dowel. With twice the cross-sectional area, this would appear to be a more viable option. However, a wood axle rolling against wood has a lot of friction and the wheels don’t spin as easily as desired. The tack through the magnet may also be long enough to interfere with the axle. A plastic or metal sleeve could help to reduce friction and wear, but the larger axle also requires a deeper railcar undercarriage that tends to drag on the track over ramps and arch bridges.

Shown are the cross-sections and axle configurations for standard model trains, three of the wood train manufacturers, and wood wheels with either a 1/8" or 3/16" wooden axle. The Brio^® cars have an axle that captures the wheel. Learning, Curve^™, Whittle, and others rely on an axle with knurling, barbs, or rings to retain the wheels.