HI M.!
First off, Have a great trip!! Sounds like you deserve some time off.
I've traveled with both my kids when they were infants, and here's what I did.
1) Take the carseat. Some of them are hard to get buckled in, but your child will feel comfortable in it. Holding a child for that long will drive you both nuts. If you sit right next to her, and she's facing backwards, you'll be able to play with her the whole trip. Of course, you can take her out when she gets fussy.
2) Benedryl! If you give your baby the proper dosage of Bendryl before the trip, you'll all have a happier trip. It is probably the safest drug on the market -- even more so than Tylenol -- and does two things for most kids: one, as an antihistime it helps keep nasal and ear passages open and clear, which helps with equalizing the pressure in her ears for take off and landing. (Also, if she uses a bottle or is still breastfeeding or uses a pacifier, make sure she is sucking during these times which also helps). Benedryl also makes most kids a bit sleepy.
3) Try to keep your baby on her regular schedule. Just keep her up longer or put her down earlier -- the 'regular' times in the new time zone. If she wakes up in the middle of the night, just cuddle her in bed. Don't turn on the lights, don't play with her, don't give her any reason to 'be awake'. Most babies get bored after about 20 minutes and will settle in.
Most importantly -- have a great time, and don't forget the baby sunscreen!