Just a note: You aren't allowed to take the puppy out of the soft-sided bag/kennel during a flight, and aren't even supposed to open the bag, so I'd probably put a pee pad under a towel in the bottom of the bag, bring some moist treats along to feed her when she whined, and just bathe her (if she gets pee or poop on herself) when you get home. Other passengers will not be able to pat her (and probably won't even be able to see her considering you can't take the kennel/bag out from under the seat). This is from American Airlines, but all airlines I've flown with have been similar:
Movement of Pets During Flight
Pets must stay in their closed and/or zipped kennels under the seat in front of you at all times. Pets may not be removed from their kennel/container at any time while onboard the aircraft.