The best thing to do with your stroller is to check it at the gate. You can take your stroller through security and then use it the entire time you are in the airport. Check in at the gate before you board the airplane and they will put a claim check tag on your stroller. Then when you board the plane you just leave it right outside the airplane at the end of the jetway. From there it will get put on the airplane. The great thing . . . when you get off the plane at your destination, it will be waiting right there outside the plane for you again. You can load it up with your child and carry-ons and be off through the airport with ease.
One thing to note - When you go through security they will ask that you fold up your stroller and fit it through the x-ray machine. If your stroller does not fold up that compactly, don't worry about it. Just tell the TSA agent and they will have someone manually inspect it. I have flown with my double stroller many times and this has never been a problem. You will have to empty out your stroller and remove your child first.