I found a way to keep the Windows keyboard above my QML "fullscreen" application. What I noticed is that in non fullscreen application, the keyboard appears well above my QML application. So the idea was to simulate a fullscreen application giving the window application nearly the size of the screen. Some code will be better:
ApplicationWindow {
id: mainWindow
x: 0
y: 0
width: Screen.width
height: Screen.height + 1 //+1 because does not work if the window size is equal to screen resolution. In some way, it considers it's a real fullscreen application and the keyboard stays behind.
flags: Qt.FramelessWindowHint | Qt.Window //first flag to remove top right buttons such as close button, second flag to keep the application thumbnail in the Windows taskbar to close it if necessary.
visible: true
...
}
With that, I can open the Windowd keyboard clicking on a text field, close it, re open it, ... all that I want!