In a similar scenario last week our 2nd leg was automatically rebooked 24 hours later whilst still in the air on my delayed 1st leg into DOH (I had already checked and pretty much every other same day option was fully booked). When we made it to the gate for our original connection (12 mins running with QR staffer in tow and thankfully empty transit security), the gate agent had to add us back onto the flight as we’d been offloaded.