We take out dogs and cat on planes occasionally. The rules might be different for other countries but over here pets are definitely not sedated, and shame on any pet owner for letting them do that to your pets.
Nor are we allowed to bring the animals into the passenger section of the plane. Or cat happily travels in the cargo compartment and he always arrives looking fine.
All airlines insist on using animal enclosures that meet their standards. They don't allow collapsible cages. For out cat we use a plastic enclosure that looks something like the blue one on this website (3rd one down) :-
http://www.cat-alog.com/cat_carriers.html
Inside the cage we put his favourite soft toy, and one of my wife's old tee shirts. Wear the shirt for an hour first. This effectively puts the odour of the owner into the cage and helps him feel settled and safe.
Tip, don't feed her before the flight. Yes she'll be a little hungry, but she's less likely to be sick, and less likely to defecate inside the cage.
