This is simple,

You make sure your hole in the wheel is round and at 90 Degrees

Make sure you dowel is round, if not make them round.

Cut the dowel to the length you want it.

With a scroll saw or fine saw, cut a slot (V shape) in the end of the dowel.

Slot length should be the depth of the hole in the wheel (wheel thickness).

With the grain running the same as the dowel.

Cut a wedge from a piece of wood (V shape) to go into the slot.

 (This is the same concept is the wedge in the end of a Hammer handle).

Glue the inside of the wheel and the slot,

Put the wheel on the dowel

Drive the wedge into the slot, at the end of the dowel

Let dry, trim, and sand

When dry you will not get it off.

Just like MAGIC