I just got back from a trip with my three year old and it was the first flight where I didn't take the car seat. I was traveling alone with her and didn't want to hassle with the large car seat, on top of my daughter's liquid meds, the portable DVD player and the laptop computer. I planned the flight when I thought she would be most likely to nap. With the car seat, she always slept for some portion of the flight, but on this flight, she couldn't get comfortable and ended up being cranky.
The pros of the car seat:
* more comfortable for the child
* safer if there is turbulence
The cons:
* bulky - just one more hassle to deal with in security and getting on/off the plane
* if your child is tall, the car seat gives them easier access to kicking the seat in front of him/her
* depending on the size of the seat, it might mean less room for whoever sits in the middle seat
For carry ons - you can take a diaper bag and a carry on for your child. The diaper bag is like taking a purse or laptop along with a carry on. Each child with a ticket can take 2 checked bags, just like an adult. I'm not sure if you have an infant traveling for free if you can still take 2 bags per traveler or not. When I took my daughter on trips as an infant, we had two bags total (one for clothes and one for toys, etc.).
Have a great trip!
S.