The AutoTrace is a plugin for QGIS that allows users to digitize new features based on vertices from existing features. It essentially allows you to trace existing features. You cannot use it to trace an image directly, it use to with existing vector layer to make polygons contiguous.
The only way to trace contour from an image is to do it manually by creating new line feature and start digitizing which I know it is time consuming, but it is more accurate and faster than trying to convert raster to vector automatically and then cleaning that vector layer.
Another option is to use a DEM and extract contour from the DEM but it depends on the scale that you are looking for. If contour image covering detailed area (large scale), then only digitizing is the option. However, if you are working with small scale, you can use DEM to extract contour from it.