Little ones are allowed extra baggage with a ticket, but you really don't want to use that allowance if you can help it. Realize that it will take two hands to move a stroller through the terminal, so those hands are useless for pulling a rolling bag. A backpack is workable, though; we used one for the carseat. Forget about going carryon-only; it's more trouble than it is worth. You won't have to wait long for your bags, as you'll be last off the plane anyway. Carry singles in your pockets for tips; Skycaps are your friends, so use them. Also, a sling or snugli is very useful for boarding, it keeps your hands free to handle boarding passes, etc., while you stow the stroller and carry the carseat onto the plane.
If you don't own a rolling pullman suitcase, invest in one now. Since becoming parents, we have made it a practice to use one large (not exceeding 62" total measurement, of course) rolling suitcase for the entire family. IMO, reducing the number of bags to keep track of makes travel MUCH easier! If the weather is cold, I use plastic "space" bags to compress the stuff to fit, though it is important to watch the bag weight limit and not exceed it. (If the weight is close, the trick is to put a cloth duffel in the big bag, then transfer a couple of the space bags into the duffel and check it, too. Then you can reconsolidate at your destination before leaving baggage claim.)
In case of delays or cancellations, *always* fly with 24 hrs. worth of baby supplies in your carryon luggage. (You just never know when weather somewhere else will delay the departure of your flight by several hours.) Include big ziplocs and a change of shirt/underwear for yourself in that bag, just in case. (I always recommend a couple of cloth diapers and a little bottle of liquid soap in a big ziploc in case of airsickness; a baby can't hit an airsick bag, and a good absorbent cloth and real soap are crucial if you have to scrub up nasty stuff.)
My kid is a FF on 7 airlines. He's six now, but he had racked up more than 100,000 airmiles before he turned two, we stopped counting at that point. We fly internationally on a regular basis, and I can tell you that the trick to flying with kids is the right equipment and luggage, once you get your system down, you'll sail right through.
