Hi L.,
It looks like you've gotten some great suggestions, and I'll just add my experience to the list too! I travelled to Mexico in April alone with my son when he was 14 months. He wasn't walking yet, and I didn't purchase him a seat since they were so expensive.
We took a non-stop flight, and I'm really glad that we did. The hassle of getting him on and off the plane with all the gear, extra take-offs and landings, would have been much worse than a solid 5 hours on the plane. I was really nervous about flying with an active baby, and I bought special, new toys for the trip, but it turned out that he was really interested in the flight magazine, safety card, water bottles, etc. He barely even played with the new toys!
The one thing that I brought that was helpful was lots of his favorite snacks. Popping goldfish crackers into his mouth so that he'd chew and swallow also helped during take-off when he didn't want to nurse or drink from his sippy cup. Sometimes you just can't make them, you know?
The other thing I can offer is that we were traveling during Spring Break--so like you, the planes were packed. This also made me nervous, but it turned out that traveling during the peak time meant there were a lot of other families traveling. Our flight down had a family with a two and a four year old sitting next to us, and a family with a four and a six year old in front of us. When I apologized for my son's screaming when he got so tired but wouldn't settle into my arms and nap, the mom next to me just said, "it's OK, we've all been there." She was so kind. Yes, we did get the nasty, annoyed looks from people on the flight, but there were also some very sweet people who offered to help me with carrying the diaper bag, or complimented me about how efficiently I got through security with the baby and stroller. I like to remember those positive people over the ones who seemed irritated with us.
And I guess the best piece of advice I can offer is to let your son be as active as he can be when he can be. My son hates being confined, and at the age where they're crawling or just starting to walk--they want to move. For me, this meant letting my son be on the floor of the plane for periods during the flight. I was completely disgusted at how dirty it must be, but it kept him happy, and I just wiped his hands with antibacterial wipes when I picked him back up. He was curious about how the seats bolted down, and he just wanted to pull up on the seat instead of sitting on my lap the entire time. Also, while waiting for our flight, I took him out of the stroller, so that he could look out the windows or at the gift shop stuff.
Flying with a baby is hard. You probably won't be able to match flight times with nap schedules, so your child will become a little "off". But just remember it's just a period of time. It might be a nightmare of a day, but it's just a day, and you'll get through it! Thinking in terms of "just a day" helped me get through traveling by myself with my baby. Good luck and have a great trip!