Absolutely not. I don't know why anyone would want to have the hassle of bringing and lugging around car seats that you aren't even allowed to use on any of the Disney transportation. If, by some odd reason you do have some type of emergency that doesn't require an ambulence, but a cab ride, you can always request a cab with car seats. I would never lug around car seats for my kiddos for no reason.
If she was over 2, I'd probably say forward facing on the plane would be fine though she'd still be rear facing in the car. Although, I'd feel sorry for whoever sat infront of her because she'd probably kick the crap out of the back of their seat. 

