I've flown with Morgynn before with him in cabin. I try to avoid it but when I'm gone for a week or more, it's unavoildable as he's my ESA and I need him for extended periods. First off, while they cannot charge you extra to bring him on board, take it upon yourself to book a seat with extra leg room. Usually the seats right before first class is best. Morgynn has a solid stay and curls up tight but I can't imagine him fitting comfortably in any normal leg room seat.
Make sure she is super tired. I let Morgynn run around for two hours before bringing him to the airport. He's generally fantastic around big crowds and I didnt have to give him any meds or anything. He was very nervous upon takeoff the first time but settled quickly. Touch downs are also a little jarring.
Buy a stupid vest. I know it's unnecessary and stupid but it makes a difference. The first time I tried to fly with Morgynn, I was unable to because despite his paperwork being in check and everything being legally complied with, they wouldn't beleive he was an ESA and I ended up having to leave him at home or I was going to miss my flight. The second time around, I bought a vest, they didn't even blink an eye or stangely enough, have to do the ridiculous amount of phone calls they did the first time around. (-_-)
This is of course, assuming that your dog is pretty bomb proof. If not, do not go anywhere near an airport. Lots of noise and rude people. Parents just let their kids walk up to Morgynn, people either cooing over the dog or giving you a stink eye for having one, little obviously fake 'ESAs' in handbags or on leashes barking at your dog. There's a lot of opportunity for things to go wrong and dont put your dog into that situation unless you know she can handle it without a reaction.
Also. STOP TAKING YOUR DOG TO PUBLIC PLACES. It's an ESA, not a service animal. The only places you get to bring them where normal dogs are not allowed is on airplanes and FHA-governed housing. Only service dogs get full public access. Train your ESA in public events where pets are allowed to attend, not in other settings. Keep in mind that to fly and to get housing with your ESA, you need letters from a doctor and the flying letter has to be updated on a yearly basis.