Bobby Zamora's late goal was enough for Harry Redknapp's side, who had looked up against it when Gary O'Neil was sent off on the hour mark.
They return to the Premier League at the first attempt and are 2/5 to survive or 2/1 to be relegated with the online firm.
Football League sponsors Sky Bet make Derby 100/30 to gain compensation by securing promotion at the end of next season, and they're 11/1 to win the Championship.
Sky Bet's Sandro Di Michele said: "Derby will need all summer to pick themselves up from Saturday's blow but such has been their improvement this season, it's perfectly possible they can launch a title bid next time around.
"Our traders reckon QPR will make a good fist of it back in the Premier League and of the promoted sides it's Burnley who look set to struggle - they're 4/7 for the drop."