Definitely Continental if you're flying the dog as cargo. United, Northwest & Delta will all take the dog as baggage or cargo (if you're not flying on the same flight) during most of the year. If I'm flying with the dog, I prefer Delta. So many of Uniteds flight are operated by U.S air anymore...and they won't take dogs. Northwest is OK...I just don't like their "hubs". Continental is the only one that will fly the dogs all year.
I heard continental is pretty good. But I personally don't have any experience with a dog in cargo. I think it can be pretty traumatic for any dog traveling in cargo.