Almost every TV family has the standard pet, and Ladybird is definitely a major pet for the Hill family.
I will say, Hank Hill really loved Ladybird. He would do things for that dog that he would not for his son or his wife.
I never thought Bobby really liked Ladybird. I guess it was fitting that he became temporarily allergic to her.
Unlike her human father, she apparently had something narrow in her reproductive organs which prevented her from having puppies.