I'm not sure about a show, but there was a mini-Blythe doll collab with Littlest Pet Shop in the past. They made several dolls, though they didn't come with pets, who were themed around the toy line (the matching pets were sold as separate toys). Maybe the show you've found was a tie-in with that line?
Edit to add:
Blythe was bought by Hasbro in 1991, it looks like. This is the same year that Hasbro acquired Kenner (the original LPS manufacturer). I wouldn't be surprised if the link was a while in the making, to be honest.