We just got back from a week-long trip to Maui with our 20-month-old daughter. We're on the east coast, so it was a 6-hour time difference. Here is our experience.
Going over, we left early in the morning--had to wake DD up at 4:45am. She didn't sleep at all during the first flight, but then she took her regular nap at the beginning of the second flight. We bought a seat for her and brought her car seat. As long as we were entertaining her, she was fine. We brought tons of books--a few old favorites and lots of new ones. I also bought her 3 new toys that we got out on the airplane. We also brought lots of snacks, which was fortunate because we didn't get any meals on our flights.
I didn't find we needed to have her walk the aisles on the plane; for her, it was enough to walk through the airports. We were all exhausted when we arrived, but we managed to keep DD up until a reasonable bedtime. She went to sleep with no problem at all because she was so tired.
She woke up early, between 5 and 6am, the whole week. We got to see lots of sunrises.
She was always wiped out by her naptime, though, because of all the fun, sun, swimming, etc. She took better naps than she does at home, a combination of all the activity and the fact that the hotel room was so much darker than her room at home. We kept bedtime flexible, given that it was vacation, and we never had difficulty getting her to sleep at night. DD didn't seem to have a great appetite during the trip. I think she was too distracted with attention from her grandparents and uncle, and all of the sights to see during meals (as opposed to our boring old kitchen).
The flights going home were much easier. Our first flight left late in the evening, and DD slept the entire 6 hours. She then slept the first two hours of the second flight, but we ended up waking her up so that she would be able to go to sleep at a reasonable hour.
She slept fine the first night we got home. Actually, she slept until 10:30 the next morning. We probably should have woken her up, but DH and I were so tired. Since then, her naps have been normal, but her bedtime has been a struggle. I'm not sure if we're trying to put her to bed too close to her normal bedtime. I'm going to try keeping her up a bit later tonight. She's been sleeping in about an hour later than normal, too.
We didn't use a carrier during this trip because DD pretty much refuses to be worn. But when we traveled when she was younger, our Ergo and mei tai were terrific--especially for getting through the airport. If you're bringing a stroller, you can pile your carry-ons in there and just wear your child. They've never made me take her out to go through security, although that might depend on the airport. Also, remember that things like diaper cream count as liquids, so you'll want to go through your diaper bag ahead of time.
I hope you have a great time!