Just noticed you should be using Serial2 for pins 18 and 19...
Nextion myNextion(Serial2, 9600); //TOUCH A ---> TX to pin 18 and RX to pin 19
Note that on the Due, pins 0 and 1 are 3.3V ... pin0 (RX0) has already been level shifted to 3.3V using a single bus buffer.
EDIT: Oops ... should be
Nextion myNextion(Serial1, 9600); //TOUCH A ---> TX to pin 18 and RX to pin 19