I think the first thing to do is make an RGB colour ramp. You can get the RGB values for the colours in the ramp by loading the colour scale image (the one you posted above) into QGIS and then starting the raster Value Tool plug-in. As you move the pointer over the image you will see the RGB value for the point under the hand-tool being reported in the Value Tool window.
Next, you will need to make a table something like the one below. The first column contains raster values and the other three are RGB triplets. Save the file as a plain text file called (say) "ramp.text". The columns may delimited with spaces or tabs, in the example below I've used tabs. In the example table I've left it to you to replace the "x"s with sensible intermediate values.
5539 0 0 0
x 2 67 0
x 4 120 11
x 103 177 64
0 255 255 255
-x 201 111 61
-x 118 2 2
-x 79 0 0
-6880 0 0 0
Apply the colour table to the difference raster by going Raster -> Analysis -> DEM (Terain models). Set "Mode" to "Color relief" set "Color configuration file" to point to "ramp.txt" and give your output GeoTIFF a name. Then hit "OK" and see what you get.
There are other ways of colour rendering one-band rasters in QGIS, but this is the one I prefer. This way of working uses gdaldem color-relief, for more details see:http://www.gdal.org/gdaldem.html#gdaldem_color_relief