Somehow I believe to recall there does exist some ind of "draw parallel line" plugin for QGIS.
Could anyone please point me to - I can't find it :-/
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It's in the Sextante tool box. See the accepted answer here: How to create a line in a given distance to an existing one?
I think the plugin you are looking for is
cadtools. You can download it using the plugin installer.
Once you have it installed it will create a new toolbar with all kinds of handy tools, with one being to create a parallel line.
First select the line using the button next to the one in the image. Then select the Create parallel line tool.
It will ask you for a distance to offset from the line. You can even use negative numbers.
The red dashed line is the new line which is offset 5m from the selected line.
Rather than a plugin, you might find it easier to select the original line and then copy and paste it. You can then move the new line around with it holding the direction, if you grab it in the middle.
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