I have traveled with an 11 pound Maltese mix and use a soft sided Sherpa backpack kennel. The biggest issue for you is that the carrier fit under the seat in front of you and the dog at least has the ability to scoot around in it. My dog learned the sound of the engines spooling up for takeoff and he'd scoot around to face forward for takeoff. I've traveled with him on AA/US, DL, and WN and had no issues from him or staff, but I follow the rules and don't push boundaries like him running loose in the gate area or taking him out of the kennel during flight. He is always quiet and I've had no behavioral situations with him ever.
You'll hand carry him through security so have him in your arms when you approach the TSA agent to show your boarding card. You'll be directed through the scanner and have a hand swipe for explosives at the end of the line and you're done. Minimize other carry-ons because you'll be busy handling your pet.
Don't do the trip cold turkey of simply putting the dog in the kennel and off you go. Make a game of it and get the animal used to the kennel ahead of time with you carrying it, and take him to ride in the car in it a couple times. Include in a side pouch a jar lid you can use for a drink of water from a fountain, a washcloth and a small toy. I covered the bottom of the kennel with a worn t-shirt so he smells his normal environment. Do not feed or water him immediately prior to travel to minimize the urge to relieve himself. Look up locations of pet comfort stations in or outside the terminals.
I've consistently found all airline staff friendly and helpful when they see you traveling with a pet. I've never had an issue with them or fellow travelers who observe him traveling with me. And in my case, my dog is a lot quieter than most kids and you'd never know he was on board.
Relax by doing some prep for you and the dog and enjoy your trip.
P.S. My backpack kennel keeps me hands free so very convenient when using the restroom. I did not want to put his kennel down on the floor to use the urinal.
If you have to, use a stall toilet as floor area bigger and cleaner than a urinal area.