The method provided by Kazuhito is far more elegant, but in case you don't have access to QGIS 3.0/3.2, here are two methods for 2.18:
Create a 2 meter single-sided buffer with OGR >
Single sided buffers (and offset lines) for lines tool (Processing Toolbox)
Polygon Centroids tool (Processing Toolbox) to create centroids of buffers.
Create a point on line layer using one of these tools from the Processing Toolbox:
- QGIS >
Random points along line
- OGR >
Create points along lines
- GRASS >
Select all features in point layer, use
Move Feature(s) tool (editing toolbar) to move them.
Check the results of either method by using
Spatial Query to select features of the points layer that intersect features in the lines layer.
Move Feature(s) tool to move them away from the lines they intersect.