The Wales Under-21 international, who signed a contract extension with Saints on Wednesday, has yet to make a first-team appearance for Nigel Adkins' side.
However, it is hoped Doble will gain regular experience at Edgeley Park as the npower League Two strugglers bid to avoid relegation.
Southampton boss Adkins said: "He's a young striker coming through the system, and we are trying to help him with his development.
"We were able to secure him for a bit longer with his contract, so that gives him the security he needs.
"Now we have decided to let him go out on loan to Stockport to help him get some league games under his belt as well."
Source: PA
Source: PA