Don't listen to anything Ian said. I have taken both of my kids flying. My son flew in our C170 for the first time around 2 years old and I still have to pry him off the plane to go home. He'd sit in the plane with his "ears" (Full size DC10-30s) on for :30 minutes waiting to go. By 3 years old he was wanting to solo. My daughter on the other hand got her first plane ride in a nice comfy, brand new Citation Excel around 18 months......and she screamed her head off (not the good way) from takeoff until landing (: 10minutes). Go figure.
Just make sure you have a car seat "approved" for aircraft and follow the seat manufacturer's recommendation on seat location and installation. As far as headsets, pick up a set of hearing protectors from a sporting goods store. Like the kind used for sport shooting, they will fit a bit smaller than intercom headsets. I don't imagine your child will have much to say anyway, right?
Plan on making short trip the first time. Maybe one or two laps around the pattern. It will take a while to get :30 minutes out of her.
For the record. My son road in the back seat of the 170 alone with no problem. He also accompanied my daughter and wife in the Excel and he loved it too. And no, he wasn't in the right front seat. Much to his disappointment.
Good luck, let us know what you decide.
NJA Capt
Oh yea...Seat belts were neither a problem in our 1951 C170 nor the 2002 Citation Excel. Both worked well with each car seat.