I would definitely take some sort of note for your niece, along with a "permission to treat". Why? Because the TSA lady asked my 5 year old a few questions to make sure that he was mine and that he knew me, etc. And it's one of the areas where having a mom as a hippie hasn't helped me, because I called my mom by first name, and DS calls me by first name, and he was freaked out by her and couldn't figure out what words she wanted (aka "she's my mom"). It was ultimately no problem, and explaining that he calls me by first name was accepted by her, plus hubby was behind us and he pointed at him and told her that he was his dad (DH likes to be called by title where I don't, though he certainly does know, and has called me the title, that I'm his mom).
Anyway, I'd hate for you to get into a situation like that where she's your niece and you have nothing saying that you have permission to take her on a plane trip.