We have traveled w/our 2 kids on a plane twice at least. Both times went fine. A little stressful but nothing crazy.
1. Bring a baby carrier like an ergo. That way, you can carry the baby through security without taking her off of you, you just have to let them swipe your hands or something.
2. Gate check the stroller so you can access it easily when getting off the plane. You can just check the car seat normally (for free too).
3. I think the diaper bag is just like your personal bag. I usually carry a backpack, I never used diaper bags I prefer back packs.
4. Take snacks like puffs and stuff. And you can take formula/water as long as TSA can test the liquid to make sure you're not going to blow up the plane.
Everything else is pretty normal as far as travel goes, just keep the baby occupied and hope that they sleep on the plane!