RC522 RFID and Ethernet Shield

Hi
I am building an rfid system at work. The system is working with arduino uno and RC522 (with a buzzer on pin 7) but things got mixed up when trying to add ethernet shield to communicate via ethernet. I am new to the ethernet shield but I learned that i cant use the pin 10 on the shield. So i changed the SDA My pinout is like this:

Pin Pin
Arduino Uno MFRC522 board
9 RST (Reset)
8 SDA (SPI SS)
11 MOSI (SPI MOSI)
12 MISO (SPI MISO)
13 SCK (SPI SCK)

And the code i use is at the end. So my question is will this pin layout work? If not what do i have to do?
Also it would be nice, if you can post guides / helps about using the shield. I need to read the same data on the serial monitor via ethernet.

I have also attached the photos of the pins.

#include <SPI.h>
#include <MFRC522.h>

#define SS_PIN 8
#define RST_PIN 9
MFRC522 mfrc522(SS_PIN, RST_PIN);  // Create MFRC522 instance.

const int buzzer = 7; //buzzer to arduino pin 9

void setup() {
  Serial.begin(9600); // Initialize serial communications with the PC
  SPI.begin();      // Init SPI bus
  mfrc522.PCD_Init(); // Init MFRC522 card


}

void loop() {

  
  // Look for new cards
  if ( ! mfrc522.PICC_IsNewCardPresent()) {
    return;
  }

  // Select one of the cards
  if ( ! mfrc522.PICC_ReadCardSerial()) {
    return;
  }

  tone(buzzer, 1000); // Send 1KHz sound signal...
  delay(1000);        // ...for 1 sec
  noTone(buzzer);     // Stop sound...

  
  // Dump debug info about the card. PICC_HaltA() is automatically called.
  for (byte i = 0; i < mfrc522.uid.size; i++) {

    Serial.print(mfrc522.uid.uidByte[i]);
  } 
  Serial.println();

  
}

based on the code: http://playground.arduino.cc/Learning/MFRC522