UA (at the stations I go to) provides sturdy plastic bags for car seats, I would re-use them on WN. Other times checked them in plain (be sure to buckle it up and tie up hanging straps) - they will come out all right.

If it's a really spendy carseat I'd suggest buying a cheaper Cosco model at Target/WalMart and using that for travel, to avoid any fear of damage/abuse of your main carseat.