Stylus

The tracing bit, or stylus, is an old router bit or similar object of the same diameter.  The bit is covered in tape to make its diameter slightly larger than the cutting bit and to protect the template or original carving from damage.

I pre-drilled holes in the carving mount for wood screws to hold the original or blank to the mount.  The mount has a slot in its base to allow for adjustments needed to line up the template and blank.

A more powerful router would certainly work.