Calibration of the fuel gauge really has nothing to do with that specific problem. But of course any gauge can be checked for accuracy with a calibration performed on it. Though, where did you come up with the fuel gauge needing a calibration anyway? Yes the possibility of the fuel gauge becoming faulty might be a slim chance but in this case, that's not the solution to solving the problem.
But if you really are concerned that the fuel gauge's "calibration" is in error and plays a role in the problem that you are encountering then by all means swap out the fuel gauge with a new one? Though, you do that and the problem will still be there, with the fuel gauge not indicating correctly, just telling you.
The problem will more than likely be with the fuel tanks internal fuel gauge sending unit. Reason being is that the fuel gauges sending unit is not receiving the correct voltage to give the proper readings for the fuel gauge to indicate a correct reading on the meter, in reference to the fuel sending units float component not giving the correct level of fuel/gas in the fuel tank. It basically has to do with the fuel tanks sending unit's internal components going bad.
But like I said....take it to the dealer and let them handle it.