6:00 a.m. is correct. If you want a room before 6:00 a.m. (and one is available), you'd have to pay the daily rate for the extra day.
But you can arrive any time after 6:00 a.m. to check-in. Even if your room isn't ready yet, you can get your park tickets (if you booked a package or arranged to buy tickets at the reosrt even if it's a room-only reservation), set up a room charge, etc. You'll get your room keys, but they won't actually open any doors ... yet. They'll give you a card with a phone number. You can call this number after 3:00 p.m. and learn your room number. This way, you can go straight to your room and not have to wait in line at the front desk again.
I forgot to mention that you can also check your luggage with the resort so you don't have to leave it in the car or drag it around with you.