It really depends on your 3 yr. old. I have traveled from MI to CA twice with my daughter...once when she was just over 2 and once when she was just under 3. I was set on taking the seat on the plane (also because we needed it while there). I was traveling by myself. I had one backpack on my front, one on back, car seat, and kid on a leash! (I always thought these were crazy, but really was necessary and gave me piece of mind in the crowded airport).
Anyway, I thought it would be easier for my daughter ot sleep with the seat, but all she wanted to do was to play, read, etc. on the tray! Because the seat lifted her up, the tray would not lay down and she couldn't use it. we were lucky that the plane was not full, so she could sit in a different seat for a lot of the time. I decided after that, that I would not bring the seat on the plane again.
If you think your daughter will actually sleep, and will only want to do activities in her lap rather than coloring, etc., then bring the seat. If your little girl is miss independent/busy like mine, you may be better off without it.
One other thing. I was carrying the seat through the airport with two hands, one on the back and one underneath. after that trip, i saw someone carrying one by fastening the harness and using that as a handle. duh...why didn't i think of that!?