I had to do this when I moved from MI to CA - and at that time was told to ship it without a car cover on. Dust/dirt could get caught under the cover...then you have make-shift sand paper ruining your clear coat/paint. If you can find a reasonable enclosed carrier, that would seem to be the best bet. If it's too pricey, just get it detailed before, and after transport and you should be fine. Welcome to LA