For anyone else trying to get this to work on a Due the above is correct except if using Serial1 you should configure USART0 not USART1.
Serial1.begin(9600);
USART0->US_MR = US_MR_USART_MODE_NORMAL | US_MR_USCLKS_MCK | US_MR_CHRL_8_BIT | US_MR_PAR_NO |
US_MR_NBSTOP_2_BIT | US_MR_CHMODE_NORMAL;
Would be very nice if the Serial.begin(speed, config) function was ported for the Due!