Hi L.,
Well, we have 3 kids ages 5 and under...and since they've been able to walk have always bought them their own seats, for several reasons (not necessarily in this order!):
1) We usually fly at night - it's hard to sleep holding a toddler and this way they can sit in their own car seat and get some much needed sleep as well.
2) It's no fun for anyone chasing a toddler up and down the aisles.
3) It's the safest way to fly them.
That being said, we used to have to drag on 2, yes 2, HUGE carseats!! OUCH! Then, we finally learned about a harness-type seatbelt that attaches directly to the seat and uses the airplane seat belt as well. It's GENIUS!! It's just like a 5-point harness from a carseat, and it's made specifically for airplanes. We used it just recently on a flight from Los Angeles to Tampa, and it was absolutely fabulous. Fits in the diaper bag or in our case my purse!! You can get one at: http://www.kidsflysafe.com.
If you need her car seat where you are going...then you can buy large car seat travel bags at Babies R Us...they're pretty durable and are big enough to fit the car seat and other stuff like blankies, etc. Also, if you are checking a stroller at the gate, make sure you get ALL your parts back. Lots of times trays and cup holders get taken off, and you don't realize it until your long gone...and that stinks!
One note - if you can, pack her her very own little "backpack"...with toys, coloring books or anything "cheap" so if it gets lost no harm done. I keep a stockpile of things from the dollar store or the $1 section at Target...stickers are awesome too. Also pack some snacks she loves or ones that she doesn't always get as a special treat. It will keep her busy for most of the ride! I never let the kids see what's in their backpacks until the plane takes off - and they love the anticipation and surprise!!!
Good luck!