Rangers boss Ian Holloway recalled Doughty from a season-long loan at Swindon Town in January, insisting he rated the 24-year-old highly and wanted to give him a chance in the first team.
However, Doughty started just two matches under Holloway – and has made just 12 first-team appearances for Rangers in total, nine of them as a substitute.
Swindon were the sixth club Rangers have loaned Doughty to. He was previously at Crawley, Aldershot, St Johnstone, Stevenage and Gillingham.
He has another year of his contract at Loftus Road left to run, meaning a permanent transfer might be out of League One Peterborough’s reach.
“It could be a tough one to pull off,” Fry admitted, “He’s on good money at QPR.”