I am working with OpenLayers plugin in QGIS 1.8 but I am not sure on how should I manage the CRS.
The default CRS for Google/Bing layers is WGS84/Pseudo Mercator (EPGS:3857) but I am not sure on the CRS of the new layer I want to work on.
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You should create new custom CRS and assign it to your layer(s). This quick and dirty approach worked for me after reading all the posts arround here. I use QGIS 2.8.1 and metric system, as I live in Central Europe:
Measure your x and y difference between specific point on Open Layer and that same point on your layer
Go to Settings, Custom CRS
Maybe picture is more informative, so I attached one. Hope my approach will work for you as well.