I want to use something like an Omega belt drive but with a reduction gear.

https://youtu.be/m_v1LCUSOwY
Or like that one but with a belt instead of the nylon gears.
https://youtu.be/T9QU3YQe-Sc

I am no engineer so I don't know how to use ball bearings and axles for the two linked pulleys. Can I just screw them on an 8mm axle together and then have bearings left and right? Do I somehow have to secure the axle against axial forces?