I think you can use the following simple solution:
Process p = new Process();
p.StartInfo.UseShellExecute = false;
p.StartInfo.RedirectStandardOutput = true;
p.StartInfo.FileName = "cmd.exe";
p.StartInfo.Arguments = "/c ping 192.168.1.1"; //or your thing
p.Start();
p.WaitForExit();
string result = p.StandardOutput.ReadToEnd();
System.Windows.Forms.Clipboard.SetText(result);