Hello,
Cool idea. Although it might not live up to GT Academy standards... (nice fire suit!)
My guess: the GPS shield with the patch antenna has a limited spatial resolution which will affect the precision of your measurement (depends on conditions but it's safe to assume +/- 10m error). In addition you are limited to maximum of 10 samples / second refresh rate. Add those two together and you are probably looking at half second resolution or worse.
Still an interesting project though. You can throw in some interpolation and compare with a beacon-based lap timer to see how close you can get the results... Or maybe add a 9-axis gyro/accelerometer/magnetometer to capture kart dynamics around the track?
Good luck!
Chris