The Nokia Maps API for Qt and Maps Demo itself does not have a dedicated KML parser within it. However KML is merely a "well-known" format of XML, and a series of Qt XML Examples already exist. To read KML all you would need to do is parse the <coordinates> element within each <Point> element within each <Placemark> and so on.
It gets a bit more complicated when trying to parse complex documents with <Folder>, but you will only need to do this if your input KML is more advanced. I would try reading a few simple but schematically well defined sample KML files first and just output the coordinates read. Try searching for a "Sample KML file" to get some examples.