Ok but moving the socket was not my point, I try that with your code :

main.c
Qt Code: 
  1. #include <QtCore/QCoreApplication>
  2. #include "clientsocket.h"
  3.  
  4. #include <QThread>
  5. #include <QtDebug>
  6.  
  7. int main(int argc, char *argv[])
  8. {
  9.     QCoreApplication a(argc, argv);
  10.  
  11.     ClientSocket m_ClientSocket;
  12.     QThread *thread = new QThread(&a);
  13.     thread->start();
  14.     // now we got another thread
  15.     m_ClientSocket.moveToThread(thread);
  16.  
  17.     qDebug() << "Main thread is " <<QThread::currentThreadId();
  18.  
  19.     bool bConnected = m_ClientSocket.connectToHost("10.33.17.37", 8000);
  20.     qDebug() << "Connexion done";
  21.     if (bConnected)
  22.     {
  23.         qDebug() << "Ask for Id";
  24.         m_ClientSocket.write("*rem\n*idn?\n", 10);
  25.     }
  26.  
  27.     // For testing don't do a exec() just wait for msec
  28.     // Without the processEvent() qDebug not displaying anything but
  29.     // the threadid prove the reception is done in the other thread
  30.     thread->wait(500); // After 500ms I should have the response or I give up.
  31.     a.processEvents();
  32.     thread->quit();
  33.     thread->wait(100);
  34.     return 0;
  35. }
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clientsocket.h
Qt Code: 
  1. #ifndef CLIENTSOCKET_H
  2. #define CLIENTSOCKET_H
  3.  
  4. #include <QTcpSocket>
  5.  
  6. class ClientSocket: public QObject
  7. {
  8.   Q_OBJECT
  9.  
  10. public:
  11.   ClientSocket();
  12.     bool connectToHost(QString host, int port);
  13.     void write(const char* Data,unsigned int nBytes);
  14.     //void run();
  15. public slots:
  16.   void test();
  17.  
  18. private:
  19.   QTcpSocket* m_socket;
  20. };
  21.  
  22.  
  23. #endif // CLIENTSOCKET_H
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clientsocket.c
Qt Code: 
  1. #include "clientsocket.h"
  2.  
  3. #include <QDebug>
  4. #include <QThread>
  5.  
  6. ClientSocket::ClientSocket() : QObject()
  7. ,m_socket(new QTcpSocket())
  8. {
  9.    connect(m_socket, SIGNAL(readyRead()), this, SLOT(test()), Qt::QueuedConnection);
  10. }
  11.  
  12. bool ClientSocket::connectToHost(QString host, int port)
  13. {
  14.   if (port == 0) return false;
  15.   m_socket->connectToHost(host, port);
  16.   return m_socket->waitForConnected(1000);
  17. }
  18.  
  19. void ClientSocket::write(const char* Data,unsigned int nBytes)
  20. {
  21.   if (m_socket && (m_socket->state() == QAbstractSocket::ConnectedState))
  22.   {
  23.     m_socket->write(Data);
  24.     m_socket->flush();
  25.   }
  26. }
  27.  
  28. void ClientSocket::test()
  29. {
  30.     qDebug() << "I got something here!!!" << QThread::currentThreadId() ;
  31. }
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This is the output:
Starting /disk2/local/qt/TestDebug/TestDebug...
Main thread is 3070105296
Connexion done
Ask for Id
I got something here!!! 3068005232
/disk2/local/qt/TestDebug/TestDebug exited with code 0
There is something strange with the qDebug in the second thread, it will display nothing until we call a processEvent() but the thread Id displayed in the readyRead connected slot proves that it's the second thread .

I don't know if you can use it like this in your app but It seems to work fine for me except that I can explain the strange behavior with the qDebug in the second thread.
(You have to take care of the cross thread call in a second time)

Hope it can help