The Pet Jet is a plane that's designed for pets. It has a five star chef, pet beds, and a bunch of other pet toys.
In Blythe's Big Idea, the Pet Jets premiere episode, Roger was sitting at a meeting for his airline, looking at pictures on his phone, when he saw a picture of Blythe and the pets. Getting the idea that the airlines should cater to pets the way Littlest Pet Shop does, he suggested building an airplane just for pets, and their owners. After that he became the pilot for the Pet Jet.
In It's the Pet Fest! - Part 1, they used it to advertise the Pet Fest by attaching a banner.