Can't believe you posted this! I was just getting on to post what worked for us, since I know before our trip I was full of questions, so I thought someone might benefit from our experience!
My son is 22 months old, and we took a 7.5 hour flight to a place that was 3 time zones away. I also was travelling alone with him.
There were actually 2 flights (one 2.5 hours, one 5 hours) with a 2-4 hour layover in an airport each way. It went FANTASTIC! So well! I was EXTREMELY surprised because I have one of the most active toddlers eva'! In fact, his nickname while we were away was "Destructo Lad".
OK! So here's what worked great for us:
1) Leash! I've never used one before, but bought him this great Monkey Backpack leash made by Eddie Bauer. I got it from Target for <$10. Since it was just me and we were going to Disney World, I was terrified we'd get separated. The leash was WONDEFUL for the airport - he got to walk and have some freedom, but he couldn't get too far! The first time we tried on the leash he screamed. But my husband adjusted it so it was a little more comfortable, and he never made a peep about it afterwards. He even gave his monkey kisses.
He will sit still to let me put it on him too when I say "Time to put on our monkey!"
2) Like PP suggest, lots of little, new toys or books. That kept us quite busy on the plane. My son isn't interested in coloring yet, but if your LO does like that the Aquadoodle things are GREAT! You just fill a pen with water (or dip in water if that's easier), and colors appear on the page! When it dries, you can do it again! Theya re really neat and they make travel ones that are small and come in popular characters (I got Thomas the Tank Engine). We also brought a package of little animals that cost me like $3, but was his most popular toy on his trip.
3) PORTABLE DVD PLAYER!!!! This was my most important tool, LOL! My MIL loaned it to me, and even though there was only 2 hours of battery life, it was fabulous! I waited until the toys started seeming unintersting, and then I broke it out. I would give him his blankie to hold and every single time he fell asleep after about 30 minutes! He only took 45 minute naps while on the plane, but that was enough to give him a 2nd wind and make him more agreeable for the rest of the trip. We brought several Elmo videos, and that worked great! You can also recharge in airports, if you have more than one flight.
4) Fun food. I think food almost entertained him more than the toys! We brought little boxes of raisins, and then he played with the peanuts and other plane treats. I also brought boxes of apple juice, which he doesn't get to drink at home. That felt special. When they served drinks, I asked for a cup for my son and would give him a piece of ice to play with. That was very fun for some reason.
Be creative about allowing your child to do new and different things with food and drink, and they will be very excited!
5) Don't worry about regular nap time or anything. Your child will be too excited to sleep at their normal time. However, if tired showing a video worked great! That got him relaxed enough to fall asleep, like I said for 45 minutes at a time.
6) Make sure you carry on any blankies, lovies or any other objects that help your child sleep. Familiar objects can help them relax enough to nap. Also, I brought one of the things from his room that we say "night-night" to before each sleep period (a small photo). We continued our normal night-time ritual in the new place we were staying, and that helped tons. IN fact, the first night we got in it was 1 am local time, and I was so concerned about getting him to bed that I neglected the ritual. When he still wasn't asleep after 30 minutes, I called my DH for some sympathy. He asked if I'd done the ritual, and when I realized I hadn't I quickly hung up and did it. Wouldn't you know, the monkey fell asleep almost immediately! It's like he needed to know that SOMETHING was normal!
As for time change, all I did was make sure he had the normal Awake time between nap and bedtime, regardless of what the clock said. He adjusted himself essentially! The first day he woke at 7 am on his own, after going to bed at 1 am. So I put him down for a nap around 12:00 am local time, since that's normally when he would go. He slept 2.5 hours just fine, and that gave us a pretty normal bedtime of 8 pm. When we got home, we did the same thing. He woke at 7:30 am the first day we got home, so I kept to our normal schedule. That 2nd night home he slept 14 hours, and I even had to wake him up so we wouldn't get too off schedule!
We've been home 4 days now, and he's totally adjusted!
have a GREAT time!!! Don't stress too much. Our LOs are growing up so fast and are more mature than we realize! In fact, we traveled with our son in August, and I can't believe how much easier he is even in the 3 short months since I traveled with him last! I'm so proud of my little boy, and I know you'll have many opportunities to be proud of your LO too. Have a WONDEFUL trip!