This would be good to have, but a little more complicated than you describe here. It will need to recursively include other variables like spatial_ref and bounds variables linked to any of the coordinate variables.
As a alternative you can use Rasters.jl to get a Raster from a layer of a netcdf RasterStack and write it to a new netcdf file. This will make a copy of the orgvar variable and any attached coordinate and bounds variables:
write("new.nc", Raster("original.nc"; name=:orgvar))
You can change the metadata as well if you need to, though it could be easier.