The benefits of having a separate seat are pretty straightforward: you and/or your wife won't have to hold her the whole time. In my daughter's case that also means that she's a lot more willing to stay put/sleep than she might be if we were holding her. Also, with another seat you can check more bags.
To solve the carseat/stroller issue we got one of these:
Sit'n'Stroll
It's a combination carseat and stroller. While it's a jack of two trades and master of neither, it's pretty darn convenient when traveling. One thing to note: if you do get your daughter a separate seat, they'll make you put her in the window seat instead of between you and your wife, which kind of sucks. Carseats DO need to be FAA approved, but when we traveled all the flight attendants immediately recognized the Sit'n'Stroll so that was convenient.
Have a bottle and/or pacifier ready and waiting on takeoff and landing to help your daughter's ears when they pop. It will also help distract her.