Use her car seat on the plane, and she might sleep through part (or most?) of the flight. I'm not sure if you breastfeed or bottle feed, but feeding her will occupy some time. If she was older (6 months), I'd suggest you taking a couple jars of food or cereal for her. But since she's so young, I can't do that.
I don't know, at this age my daughters were really laid back, go with the flow kind of kids. When the seat belt light on the plane is not on, you could hold her and play with her, etc. Then put her back in the car seat when you're required to wear your seat belt (take off, landing, turbulance, etc.) and hopefully she'll get some sleep!