I see there were plugins in the past that may have done this such as qgis2kml and qgis2google, but they no longer exist.
[GIS] way to export the style, along with a shapefile, to a kml in QGIS
exportkmlqgisshapefilestyle
Related Solutions
Assuming your shapefile contains point-data and you have categorized this points by field in the data-table (see screenshot 1) you can install the MMQGIS plugin and export als KML file (see screenshot 2).
Result is shown (partially) as screenshot3
screenshot 1:
screenshot 2:
screenshot 3:
Best Answer
You can use the MMQGIS plugin. (http://michaelminn.com/linux/mmqgis/). In the Menu "Import/Export". select the option "Google Maps KML Export". It works for me. You need to keep in mind that if you are converting a polygon with a lot of vertex, Google Earth will not be able to visualize it properly.