QGIS does not only serve as a frontend for the QGIS server, but it can also serve as a frontend for other similar servers. GeoServer is one of the most popular ones, and you can configure it from QGIS, upload layers, or even edit the style of a GeoServer layer using the QGIS symbology tools.
For this recipe, you will need the GeoServer Explorer plugin. This can be installed using Plugin Manager.
You will also need a running instance of GeoServer. We will assume that you have a local one running on port 8080, but you can replace the corresponding URL with the one of the GeoServer instance that you have available, whether local or remote.

zipcodes_wake.shp layer and style it.zipcode_wake.shp layer and drop it on the catalog item in the GeoServer Explorer. The layer will be uploaded and added to the default workspace of the catalog.http://localhost:8080/geoserver/web/.The GeoServer Suite plugin communicates with GeoServer using its REST API. By linking QGIS with the GeoServer REST API, it allows you to easily configure many elements that, otherwise, should be configured manually, such as the styling of layers.
The Geoserver Explorer plugin has a lot of features to work with GeoServer. Here are some additional ideas so that you can explore them. For more information, check out the plugin help at http://boundlessgeo.github.io/qgis-geoserver-plugin/.
Once the layer is in the GeoServer catalog, you can edit its style without having to upload the layer again. Just open the Styles branch in the explorer tree under the corresponding catalog and double-click on the style to edit, or select the Edit... item in the context menu that is shown when right-clicking on the element:

The QGIS symbology dialog will be opened, and you can edit the style in there. Once you close the dialog, the style will be uploaded and updated in the catalog.
Don't have a Geoserver instance, it's pretty easy to setup for testing. See http://geoserver.org/ for details.