Two quick'n'dirty approaches I've used, recognizing that KML line and point styling are much more limited than QGIS, so that the best you could ever hope to transfer automatically in terms of, say, line styling, is colour and width -- and that's what a simple QGIS export already does.
First, if you want to display in GE just a couple of vector layers, export the features as KML. Then, in KML, manually create a set of styles that represents how you'll want to see things in GE, which will likely be simpler and different than how you styled in QGIS. Using search and replace in your favorite editor, or a script if so inclined, replace the
<Style>...</Style> lines in your export with the corresponding
<styleUrl>s. QGIS kindly keeps the whole style block in one line, making this easier.
Second, if you want to display either a complex map with the QGIS styling intact, or a raster layer, it's easier if you export it as an image and then bring it into Google Earth via Add Image Overlay. This is then draped over GE's terrain so you can visualize it in 3D etc. I'm sure if done right, the correct positioning info of the QGIS export could be imported into GE along with the image via geoTIFF or a world file, but I always export one specific layer extent and so I copied over the bounding box info manually when this didn't work as expected for me the first time around.
(Realize this is old, but stumbled across it and thought might be useful...)