Joanie, since we have never lived near family since we have had kids, we have traveled by plane more times than I can remember with our kids. Both Avalon and Austin were on planes when they were six months and I think Avalon was on a plane for three separate trips before she was even a year old. And we've traveled at least once, usually twice a year by plane since then. At any rate, it feels like old hat, but like Kirsten said, it's simply exhausting. I found that it got harder as baby got older because of the desire to crawl and later to walk and later to run around when they needed to be staying in your lap. When they get old enough to watch movies, that's when things settle back down a bit. But really, gone are the days of taking a book or a project on the plane and relaxing or napping! You really do have to be ON 100% of the time whether it's entertaining her constantly, changing her diaper in your seat (seriously, don't try to change diapers in the airplane bathroom), feeding her, nursing her, or holding her while she sleeps. We never took her car seat on the plane (we always check it) and the first time I traveled with Avalon, I took the boppy for her to nap on, which was nice, but bulky to carry around. I never take a stroller either, just my mei tai- you can go through security with her in the carrier if she cannot walk (don't put shoes on her though, you'll have to take them off). But if you do want a stroller, remember that you can gate check it. Be sure to bring extra clothes b/c it's almost a guarantee that you'll have a blow out or barfing incident or both if you don't. It also tends to be chilly on planes, so dress her a bit warmer than usual or in layers. Bring plenty of diapers (we do cloth even when we travel, even on the plane as long as you'll have access to a washing machine it's not problem, just more luggage). Bring exciting, new toys and foods as well as favorites. Nurse when taking off and landing.
But all this aside, your flights are very, very short so you'll have no issues, I'm sure. It is likely you'll get her to fall asleep and she'll stay asleep most of the trip b/c of the noise. My spirited dd would be wide eyed all through the airport and onto the plane, but once I nursed her on take off, she would fall asleep every time. It's really longer flights that are the challenge when you have to be entertaining a squirming, complaining, mobile baby. I honestly think the worst age I've traveled with is 11-13 months- the just learned to walk age. You'll be fine.