Ok, that was easier then thought:
Apparently dup2() (never heard of it..) can redirect stdout and stderr to another (file or socket)descriptor (sorry, never heard of that either... ).

Whenever the QTcpServer gets an incoming connection, a incomingConnection(int handle) is emitted. This handle can be used in order to redirect all stdout ans stderr over a newly created socket.
Qt Code: 
  1. void Server::incomingConnection(int handle)
  2. {
  3.     Client *client = new Client(this);
  4.     client->setSocket(handle);
  5. }
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In client:
Qt Code: 
  1. void Client::setSocket(int descriptor)
  2. {
  3.     socket = new QTcpSocket(this);
  4.     socket->setSocketDescriptor(descriptor);
  5.  
  6.     dup2(descriptor, 1); // stdout
  7.     dup2(descriptor, 2); // stderr
  8.  
  9.     qDebug() << "This text ends up at the telnet-session of the connected client";
  10.  
  11.     // connect socket signals to slots
  12.     connect(socket, SIGNAL(connected()), this, SLOT(socketConnected()));
  13.     connect(socket, SIGNAL(readyRead()), this, SLOT(socketReadyRead()));
  14.  
  15.     qDebug() << "Socket created";
  16. }
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