We just did a great deal of traveling with our 18 month old. We never bought him his own seat, but usually the airlines were very accommodating and they would let us bring his carseat on if the flight wasn't full. We just wheeled the carseat and stroller up to the gate (actually down the gate to the door of the plane). You can check your stroller at the gate and then they stow it and have it ready for you when you get off the plane (or soon after). My son is really small for his age, so when we couldn't bring the carseat on (twice in 6 flights)we checked it at the gate and then he sat in our laps (mostly mine). He pretty much slept a great deal of the time and the flights we took varied from 1 hour to over 5 hours. The biggest thing would be to bring things for him to do so that he does not get board. Also, I know that you can get convertible carseats for flight that have a handle and wheels and fold-up and they might be easier for you. I don't know how much they cost because we were fine with doing the lap child route. As for ID. For the first flight I brought his birth certificate because they said they needed it to make sure he was under 2. No one asked for it (on any of the flights). They just asked his name and how old he was. If he has his own ticket this may be different, but I would think you could use his birth certificate (or a copy of it) as ID.
I would suggest that if he drinks out of a sippy cup and not a bottle you still bring the milk in a bottle and then bring an empty sippy cup along and pour the milk into it. We had no problems getting multiple bottles through for our son's milk but we did have problems with his sippy cups that he drinks water out of. Most of the time we had to dump out the water and then buy water inside the terminal. Most of the food and snacks we brought for him were fine though (just don't bring anything like yogurt. I don't know about baby food jars since he eats whatever we're eating).
For the most part all the airlines and airports were very helpful and accommodating. My son was also a great flyer and didn't really cry or fuss. He was more fidgity than anything and we needed to constantly find things for him to do when he was awake. He wanted to walk all over the place.
I hope that helps and answers questions. If you have any more just ask. Sometimes I think it depends on how far you're traveling. Oh, all our flights were outside of the state and all over the country and we didn't need any note about taking him out of the state.
Also, I've heard rumor that on really full flights so airlines try to get parents to give up the seat they bought for their child so that a full paying adult can have it. If you want him to have his own seat make sure you stick to your guns about keeping it. You did pay for it after all.
Good luck and have fun. It should be a great experience (I hope). I'd love to hear how it went.