We went to Florida from NY in July and my Daughter was 18 months at the time.
I would absolutely tell you to buy him a seat.
At his age, he will not sit quietly on your lap for 2 hours!!! It was even a bit trying for our daughter, but she had her own seat by the window...(They have to go there if you are using your car seat). Between the food I brought for her, the animal crackers the airline gave her and all her Elmo books, she did really well. IDK what airline you are flying on, but if it is Jet Blue, they have direct TV on the plane so he will be able to see many children's channels during the trip also.
But I brought my laptop and she watched her own DVD while on the plane. That is a bit bulky for you, but if you have a potable DVD player that you can slip in your bag, that may work too.
As far as getting around with all your stuff and the baby, that is hard. I will suggest that I used the Space Bags storage bags for mine and my daughter's clothing. It really helped b/c I got all our stuff into one suitcase that way. I even put her stuffed toys in the bags and they all did well in there.
We took her stroller and her car seat...UGH
But of the 2, the car seat was the better choice. I did not want to rent and get something dirty that I wouldn't have wanted to put her in.
I did see the same cart from "One Step Ahead" that the car seat attaches to and almost bought that too, but since I had my husband and my nephew to help, I opted not to.
You are going to have a bit of frustration going this alone no matter how you look at it.
Can someone go with you to help you get your things out of the car and into the airport?
Once you get in there, there are carts that you can rent so you can put everthing on it to get around....
You will need to have your son in some kind of a cart or stroller otherwise your arm is going to fall off!!
If you are not going to take his stroller and you will not have any help, then the $100 cost for the cart from "One Step Ahead" will really be worth it for you.
When you go through security, you are going to have to take your son out of the cart, take your's and his shoes off, and send everything through the scanners. If you are bringing any liquids with you over 1.3 oz, they will make you take them out of your bag and they will test it. That includes his milk, juice or formula that you may be bringing.
It was not a big deal. They did not waste any of it. They had a paper like a chemistry litmus paper that they held over the opened bottles and then they put the strip into a machine that tested it.
Be mindful that if you are taking suntan lotion, creams, liquid make-up....ANYTHING liquid in your carry-on bag, you will have to take it all out or they will confescate it when it goes through the scanners.
If you buy your son a seat, your son's diaper bag is his carry on bag...so you can have your own.
If you take the cart for the car seat, or a stroller, there is no cost for these items and you can take your son in them right to where you board the plane, Then they will check it in for you at the plane and get it back for you when you leave.
I would call the airline ahead of time and see if they can help you out with the baby and your things.
I am sure there is some kind of service to give you a hand.
Don't struggle on your own!
Call ahead and see what they can do for you.
If I can help you out with any other questions you may have, just write back!
Good Luck,
P.