J.M.
We flew from NY to Vegas with our 13 month old. We didn't do the car seat, but made sure to have all 3 seats. She slept between us. Bring LOTS of diapers and extra wipes for sure. I also brought stickers to keep her fingers busy, and plenty of snacks. We had some of her favorite books and some new books, as well as a DVD player. Of course, any meds. your baby needs, and I always have bacitracin and cortisone cream in our bag!
I used an equipment rental company for all the needs when we arrived. The company I found (in Vegas) included a bag of books, a box of toys, crib, high chair, monitors, all bedding, and a car seat. We only needed to bring her stroller and any other necessities. Might be something you want to look into...
Above all, stay calm and enjoy your trip. Kids are soooo adaptable!