There is at least one charter company which specializes in pets. They fly in the cabin of a bizjet in a quiet, climate controlled environment with an attendant I believe. They fly multiple critters on each flight so you are not chartering a jet on your own.

I would not want to put my dog in the cargo bay of many aircraft...while it may be air conditioned, the temperature control often leaves a lot to be desired and it can be VERY loud back there, as well as dark.