Is there a way to get the extent (bbox) of a vector layer in QGIS?
I see that I can update the extent, but I am looking for the actually coordinates of the extent.
The layer extents are available in the Layer Properties | Metadata section.
To get a bounding box in QGIS as a new vector layer:
Menu -> Vector -> Research Tools -> Polygon from layer extent
PostGIS has the ST_extent function which generates boundingbox for you. So my approach would be to export the layer to a database. if you want id,name, geom, boundingbox just do
select id,name,geom,ST_extent(geom) from your_table group by id