Layer stacking rasters in QGIS?

I had the same issue some months ago.

Use gdal_merge to generate a new file from the 3 independent rasters.

In OSGeo4W command line you can do this:

gdal_merge.bat -separate -of GTiff -o output.tif input1.tif input2.tif input3.tif 

In QGIS you can do the same with a GUI in the raster plugin "merge" tool.

You could try "Raster -> Miscellaneous -> Merge" which is a front-end for GDAL's merge_raster.py. It's part of GdalTools plugin that you may have to enable from the "Plugins -> Manage plugins..." dialogue.

Geoprocessing was moved to processing toolbar in QGIS 2.16, as you can see below: