Reds Devils boss Steve Evans told the club website: "We tracked him from last season and I knew Neil Warnock would have a number of clubs chasing him.
"He has a lovely left foot, takes defenders on and I think he will be a very good signing for us."
Doughty said: "[QPR manager] Neil Warnock told me a few clubs wanted to take me on loan but gave me the opportunity to train at Crawley.
"Having spoke to Steve and seen for myself the quality of player at Crawley, I wanted to sign. This is an important decision for me at this stage of my career."
Source: BBC Sport
Source: BBC Sport