Well, it's a gamble. Because if the flight isn't full, she can ride in her own seat for free. Just bring her car seat right onto the plane and buckle her in like it's the back seat of your vehicle. If your airline has assigned seating, ask the person working at the counter just before you board if it's full. If it isn't, make sure to request that the window seat next to you remains empty (they'll insist on putting the car seat next to the window for safety reasons).
If there is NOT assigned seating and you find that the flight isn't full, simply bring the car seat on board and buckle it in next to you. Everyone else will settle elsewhere.
If the plane IS full, you'll be able to check the car seat at the gate and keep her on your lap.
I've flown with my kids several times and I'll tell you that having their own seat is GREATLY preferred. Three hours is a long time to keep a 14 month old in your lap, even with your sis there to help. But it all depends on her temperament. My kids both slept much easier in their car seat during the flight. It's familiar and they're used to sleeping there while traveling. And being buckled in kept them from wanting to squirm out of my lap constantly.
Of course, I'm ignoring the whole safety aspect, but I'm sure others will address that. I wasn't too concerned myself. Really it was about ease of travel and for me, the car seat was the way to go. Financially, however, we were a little restricted so we ended up gambling on open seats and we almost always got one.
Best of luck to you!
-S.
P.S. Be sure to fill a bottle/sippy with something tempting for her to slurp down while ascending and descending. It will help keep the pressure from building in her ears which can be excruciating.