The QT Quick compatibility plugin 1.0 allows you to use "import QtQuick 1.0" at the top of your QML files. Otherwise, you need to use the "old" standard of "import Qt 4.7". Sounds like you do the former, so if you don't have the plugin installed, your QML files can't be loaded and the app doesn't start properly.

So, you need to add that plugin to the dependencies in the debian/control file, as you tried to do. But you probably put it at the wrong place when you tried, or had a typo.