Owners of larger pets beware: More headaches for your flight

For Peter Harrold and his wife, Jan, Shanti is part of the family, which means when they fly, their adorable Goldendoodle does, too.

But Shanti is too big for the cabin so she has to be checked. Typically airlines require carry-on pets and their carrier to fit under the seat in front of you, reports CBS News correspondent Kris Van Cleave.

"It is not the easiest thing, it takes a long time, there's lots of paperwork, you have to go to your vet within a week of the flight and get a health certificate each time that you do it, so yeah, you have to add about an extra hour to your arrival time at the airport," Harrold said.

Starting in March, Delta will no longer allow larger pets to be checked onto their owner's flights. Instead they'll be handled as freight.

Pets will have to arrive at the airport three hours before a flight, be dropped off and picked up at the airline's cargo facility -- which may be in a different location than passenger check-in. And the pooch could fly on a separate flight that may arrive at a different time.

"We won't do it with the cargo way, we won't do that, we simply won't," Harrold said. "We just don't have the confidence, and it would be too traumatic for us to think of the dog being handled as cargo."

Delta's change follows United which also transports larger dogs as cargo.

Sue Kazlaw-Nelson runs the airline's PetSafe program.

"We really have a better-equipped facility at cargo, and we can properly keep the animals in a safe environment and have professional staff that can look after them when they have a connection or layover rather than just leaving them out on the tarmac," Kazlaw-Nelson said.

Programs like United's PetSafe, where animals are kept in climate-controlled conditions and monitored by employees, mark a course correction for airlines, said CBS News travel editor Peter Greenberg.

"Airlines have done a terrible job for over 40 years in transporting pets in the cargo holds of passenger planes, and the statistics prove that, and the airlines just don't want to play that game anymore," he said.

Through November, 33 pets died, 23 were injured and three more were lost while in an airline's possession in 2015.

"The real issue here is connecting flights -- whether it's a passenger plane cargo hold or a cargo plane cargo hold, it gets down to the chain of custody -- who's watching that animal, who's transferring that animal, who's carrying that animal. It's a liability issue," Greenberg said.

Southwest and JetBlue won't let you check a pet. American still does, but only on certain types of aircraft and not when it's too hot or too cold.

An aircraft change delayed Harrold's trip to Florida for two days until seats on a pet friendly airliner were available. On their return to Washington, weather delayed the baggage, leaving Harrold pacing.

But from the looks of it, the wait for the reunion was well worth it.

Delta said its changes will "ultimately ensure that we have a high-quality, consistent service for pets when their owners choose to ship them with Delta cargo."

Service animals of all sizes are allowed into the cabin, a system travel experts believe will be taken advantage of as airlines make it harder to check pets.