  We use the isotropic projection of Laguerre geometry in order to establish a
correspondence between plane curves and null curves in the Minkowski $3$-space.
We describe the geometry of null curves (Cartan frame, pseudo-arc parameter,
pseudo-torsion, pairs of associated curves) in terms of the curvature of the
corresponding plane curves. This leads to an alternative description of all
plane curves which are Laguerre congruent to a given one.
