I would like to use qgis similarly as a chart plotter for dynamic data that are created by a Fortran code (being basically a ship simulator.) I have two questions: how do I integrate Fortran into qgis the best way and how can I dynamically update the plot of the position?

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Two questions here. I'll attempt both in turn:

1) Integrating Fortran into QGIS. To a certain extent this depends on your requirements, however I would recommend wrapping the Fortran in Python to then be able to update the QGIS plot. To call the fortran from python either use system calls (os.system) or pyfortran (caveat - not tested)

2) It is possible to dynamically update QGIS using python scripting. to do this use a the pyqt function:

from PyQt4.QtCore import QTimer

Put something like this together :

def updatePlot():
    #update qgis here

    #call function to get fortran results

def getData():
    #get data here

    #call function to update plot


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