We have specially made dog sweaters that hook behind their legs, so there isn't a chance of them getting all tangled in it. They do look like horse blankets in a way.
Here. We have the Traditional Sweater, and the Cable Sweater, and they've flown in them. Our dogs also like the Hoodie. The more simple sweaters and coats tend to last longer.
However, my parents dogs used to just fly with a blanket that they could burrow into.
On the other hand, if your dog has longer hair (some cockers seem to get different cuts than others), doesn't get cold very easily, or hates clothing, don't do it, the last thing you need is a very stressed out pooch. In that case, just a pillow or blanket to sleep in is best.
The dog won't need a toy if she's sedated. She'll sleep through the whole trip.