This same thing happened to me. Finally after digging through forums I found something helpful: the QPluginLoader. This doesn't fix anything, but it does have an errorString that can help troubleshoot:

QPluginLoader *thePlugin = new QPluginLoader("C:/qt/2009.05/qt/plugins/sqldrivers/qsqlmysqld4.dll");
qDebug() << thePlugin->load();
qDebug() << thePlugin->isLoaded();
qDebug() << thePlugin->errorString();

In my case the error was "module not loaded" so I opened up qsqlmysqld4.dll with the Dependency Editor and it couldn't find libmysql.dll. If you remember this is the dll that comes with MySQL. The final fix was just copying this file (libmysql.dll, not qsqlmysql4.dll) to the folder with my executable in it. Now the QMySQL driver works and I will note that for what I am doing it is almost twice as fast as the QODBC driver.