As the titel says, I found a workaround for obtaining a depth image of the camera's FOV by using this workaround. It works just perfectly by accessing the pixel data of the image with python:
pixels = bpy.data.images['Viewer Node'].pixels
BUT: This method works only when the GUI is used as well. In Background mode (using the attribute -b in cmd line) this does not work. The farest I got was to check if the image "has" some data with:
pixels = bpy.data.images['Viewer Node'].has_data
which gave me a clear false. Therefore my question is, if there is a way how to enable this data also in Background mode?
I googled a lot and the only other option I found to access depth data, is to use the Camera Data Node's depth output. However, I do not know how to access this data via python script.