Connecting Arduino due to a GPS sensor

Hi
I want to read the data from this gps-sensor https://www.sparkfun.com/products/11058
and want to print this on my serial monitor. The sensor is connected via the serial1 ports (pin18-tx1 pin19-rx1).

Now I have problems with the communication between the RX1 port and the RX port connected to my PC and the serial monitor.

int rx1pin = 19;                  // gps-rx
char gpsoutput;
const int sentenceSize = 80;
char sentence[sentenceSize];

void setup() {
  Serial.begin(9600);            //serial PC
  Serial1.begin(9600);            //serial gps
  pinMode(rx1pin, INPUT);       // Initialize LED pin
}
void loop() {
 static int i = 0;    
 // send data only when you receive data:
 if (Serial.available()>0)      
      {    
      gpsoutput=Serial1.read();          //read gps-signal
      if (gpsoutput != '\n' && i < sentenceSize)
        {
        sentence[i] = gpsoutput;
        i++;
        }
      else
        {
        sentence[i] = '\0';
        i = 0;     
        }
      Serial.write(sentence);        //write on serial monitor   
      }
}

The output is pure nonsens, or better, I don't understand the output =).
First of all the output starts with ????. And nothing follows. If I enter any char via the serial monitor, output starts to send endless questionmarks like this ?. So while I only send one char, I assume this is some data from the sensor.
I did some research and checked already the BAUD rate. Serial monitor is also 9600 and the datasheet says:
Baud Rate 4800 / 9600 / 38400 / 115200

I hope you have any ideas
Ali

You almost certainly have a baud rate mismatch with the GPS. Try them all.

increase serial monitor speed.
use print (not write) to print the string