You did not mention how the gas line is run now so for the moment I will assume it to be 1/2" black iron pipe, which is the most commonly used material for gas.
Moving the gas pipe should be a very easy job. You simply disconnect the existing gas line, install the necessary additional pipe, and reconnect.
You may call a plumber to do the job, but it should not prove difficult as a DIY project.
I would begin by lighting a surface burner on the gas range, then turn the GAS OFF at the house main and wait until the burner goes out. That will consumer the majority of the residual gas in the line after the main is turned off.
Disconnect the Flex line from the Shutoff valve behind the range.
Go below the floor and unscrew the riser to the gas valve from the top of the TEE. Unscrew the TEE from the Horizontal supply line.
Clean the threads on the end of the horizontal line thoroughly with a wire brush and apply Pipe Dope to the threads. (Make Sure the PIPE DOPE is labelled as approved for GAS SERVICE)
Apply pipe dope to the threads on the end of the new pipe.
Install a black iron pipe coupling on the threads of the existing pipe, then screw the new section of pipe into the coupling and tighten the joint using two pipe wrenches, one to hold the existing pipe steady as you tighten the coupling and the new pipe into place with a second wrench. Install pipe support hangers at not more than 5' intervals.
Apply pipe dope to the end of the new pipe and reinstall the Tee that you disconnected.
Drop the riser down through the floor at the new location. Clean the threads thoroughly with a wire brush, apply Pipe dope and screw into the top of the TEE. Tighten the pipe thoroughly then turn the Gas service valve on top of the riser OFF.
Move the range and re-attach the flex service line. (Do not put DOPE or TEFLON on the flex line flare connection).
Mix equal parts of liquid dishwashing soap and water in a spray bottle and shake well.
Turn the gas main on and check each joint by spraying with the soap mix and watching for bubbles. If you see any bubbles tighten the joint again. After all joints have been tested, turn the Service valve on at the range and light all pilot lights on the range.