Hi Gunter - yeah a scaling operation won't produce that kind of constant thickness result you're looking for, except in special cases like with a circle.
Like Finema writes above use Construct > Offset for that kind of thing rather than scaling.
As noted by Finema & Michael, use the Offset...
...but note that curves created by Offset will be Points heavy...
...so select your offset curve & use Rebuild to reduce the Points.