Thanks for your replies.
So, have I understood this correctly ?

Even if I didn't have Checked luggage, I couldn't just transit through Doha Airport (using the existing buildings, as they are now).
With toothbrush in my hip pocket, I couldn't arrive at the Arrivals gate, proceed to the transit desk, stay airside, find my Departure gate and continue on my way - either with any other Carrier, or QR for that matter.
I actually have to enter Qatar and catch a taxi from the Arrivals Terminal to the Departures Terminal ??

I just thought about this post as I was re-reading it. I bet I know the answer - if you had no Checked luggage, you would get the bus that picks you up from the aeroplane, to take you directly to the Departures Terminal. Yes ?? Would the bus do this for non-QR flights ?