Pic example thanks to /u/hateboss
Granted, the poodle wasn't white, but still.
Pet fancy (breeding dogs, cats, rabbits, and possibly other animals for show purposes) was a feature of Victorian culture. Having a tiny white lapdog definitely signifies idleness and upper class status.
Parasols were used to protect women's complexions from the sun, because milky white skin was part of the beauty ideals of the time.
It's the archetypal image of Victorian femininity, is what I'm saying. The 19th century Western equivalent of a contemporary middle/upper class woman dressed in sleek designer jeans and tall leather boots, with a smartphone and a latte in hand.