How can I send serial over RF?
In your loop function you have:

if(mySerial.available())
{
  String data = "Hello World";

  for(int k = 0; k &lt; data.length(); k++ )
  {
    mySerial.write(0xAA);
    mySerial.write(data[k]);
  }

  mySerial.write(0xA9);
}


The available() function returns the number of bytes available in the receive buffer. You say your module is a transmitter, so there will never be any data to receive (I can see the module doesn't even have a tx pin). Hence you will never transmit any data.

That said it's not a good idea to send data plain over wireless. It might work to some extent, but you'll likely get much more lost data. Look at the virtual wire library or google "manchester coding" if you wan't to roll your own.