travel by plane with a dog

Mary left a comment on my post, hotels in Germany that welcome dogs, saying that a friend of hers had seen a dog in the cabin of the plane on a Lufthansa flight. When I checked it out I discovered many airlines allow small pets to travel in the cabin.
Qantas doesn't appear to allow any dogs except registered guide dogs, who must lie near their owner's feet on an absorbent mat. In first or business they lie in front of the seat and in economy the adjacent seat is left empty so the dog can lie on the floor there.
However, sure enough, Lufthansa allows dogs in the cabin. But...the maximum weight, including the carrier, is 8kgs and may be a maximum of 55X40X20cm. What kind of dog would that be? I guess Ms Winnie the pocket beagle could qualify, but Penny sure wouldn't, so I won't be going on any planes with her in the near future.
Of course, she could travel in the hold, but the recent story about the dog who got loose in the hold and grounded a Qantas jet doesn't fill me with confidence. What if it had happened when the plane was in the air?