the debugger is a "Singleton" class. you don't need to worry about making a copy for yourself, it's guaranteed that only 1 copy will ever exist.
you need to do this:
to initialize:
OgreNewt::Debugger::getSingleton().init( mSceneMgr );
then in your loop:
OgreNewt::Debugger::getSingleton().showLines( world );
or you can save a reference to the singleton like this:
OgreNewt::Debugger& debug = OgreNewt::Debugger::getSingleton();
then just do:
debug.init( mSceneMgr );
debug.showLines( mWorld );
debug.hideLines();
etc.