Did you try inserting the character by hand? Does it get rendered as you want? Not that QTextEdit would support all of them, but I suppose that shortcut is not even listed in the list of standard shortcuts. I guess you could map a set of custom shortcuts even without subclassing QTextEdit like this:
Qt Code: 
  1. QSignalMapper* mapper = new QSignalMapper(textEdit);
  2. QShortcut* shortcut = new QShortcut(QKeySequence("Ctrl+L"), textEdit);
  3. mapper->setMapping(shortcut, QChar(0x09));
  4. connect(shortcut, SIGNAL(activated()), mapper, SLOT(map()));
  5. connect(mapper, SIGNAL(mapped(QString)), textEdit, SLOT(insertPlainText(QString)));
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