I've never understood the move to allowing any animals inside the cabin, given the number of people with serious allergies.
The best small dog/airline story I recall is a tale Buddy Hackett told many years ago on Johnny Carson. At the time, only seeing eye dogs were allowed on aircraft.
Hackett described a friend wanting to take his Yorkie on board so he approached the ticket agent wearing dark glasses, his dog's leash in one hand and a white cane in the other. He asked for a ticket and mentioned his seeing eye dog would need to accompany him.
The incredulous agent remarked: "I thought that seeing eye dogs were German Shepherds!"
To which Hackett's quick witted friend responded: "You mean this one's not?"