Scaling georeferenced image to half of its size using QGIS

From your description, I think you do not mean "rescale". Rescale usually refers to the raster values themselves, not the image size. If you want a lower resolution raster (without knowing Autocad, that's what I assume "scale factor" refers to) then the process is often called "resampling".

You can do this in QGIS using the GRASS GIS module r.resamp.stats. First you need to get the current raster pixel size (resolution) from the raster properties. Then in the r.resamp.stats module window, enter the input raster, an output raster name (or leave blank for a temporary layer). Then under the Advanced Parameters, enter your value for the "GRASS 7 region cell size". If you want the final resolution to be coarser than the original, you would choose a cell size larger than the original. For example, if your original has resolution 10 meters, and you want the result to be 1/2 the size of the original, then enter 20.

Note that this will not change the coordinates. The corners of the raster will still have the same coordinates, but there will be fewer pixels.