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 :-/
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.