The following works perfectly on my desktop debian:
xdotool search --onlyvisible --classname gqrx windowactivate key ctrl+d
It will activate the window of gqrx and synthetically hit ctrl+d, starting the dsp. On the Pi (Pi 3, Raspbian Jessie), this does activate the window, but the key press is not registered, at least the application doesn't react. I also tried keydown, keyup, windowfocus.