I have used a few carriers (sherpa, a few minor brands, and sturdibag). The sherpa was "airline approved", it did NOT fit under the seat, and I had the stewardesses fussing at me the whole flight, I was very angry (United flight, reasonable sized aircraft 6 seats wide). I gave it away.
THe sturdibag is in my opinion the only bag worth owning. You can occasionally pick them up on sale, but they are definitely worth the full retail value. I have taken these on several airplanes, including a smaller jet that only 3 seats across. You need to be in the middle seat (more luggage room), but it has fit every single time. It slides under easily, just put the carrier on the floor, and slide it under the seat. And once you pull it out again the roof puffs up to give your dog more headroom. It also comes with a quality pad, and my dogs happily sleep in theirs (I do get odd looks from people when my bags start snoring though). They're also nice and lightweight, machine washable, and can be secured in a car using the seatbelt (slide the seatbelt through the side loops, and pull the seat belt out all the way to activate the child seat "locking" mode, very secure, but also soft in the event of a crash). I have no experience actually getting in an accident with one, so cannot speak to the actually safety of the dog, but I would imagine it is one of the better options in terms of safety. Cavaliers take the Large size (and it's usually advertised using a cavalier).
My sturdibags are 2 of the best purchases I have ever made.