En fait, c'est ça!
Il a juste oublier de changer le nom de la seconde fonction!

public void doGet(HttpServletRequest request, HttpServletResponse) throws ServletException{
doPost(request, response);
}

public void doPost(HttpServletRequest request, HttpServletResponse) throws ServletException{
response.getRequestDispatcher(<ta destination>).forward(request, response);
}