What you can do is "georeference" your raster equirectangular map. I've always found the easiest way to do this is using the command-line tool GDAL, if you're comfortable with that. Depending on what installer you used to download QGIS, it's likely you've got an installation of GDAL. There is a program that you can use that comes with some of the QGIS installers called "OSGeo4W Shell", which will open a command-line shell that has all of the GDAL commands already on the PATH for you.

I wrote this blog post a long time ago to help me remember what gdal commands are useful when working with fantasy maps. The one you'd likely use for your equirectangular map is:

Code:
gdal_edit.py -a_srs EPSG:4326 -a_ullr -180 90 180 -90 map.tif
Do note, you'll need to convert your map image to a tif file, which should be possible with most image editing software, such as gimp.

Once georeferenced, your raster can be added to a QGIS project and it will show up properly.