This girl is a Shikomi-san, and the dog, Chiro, is well known in these parts.
An okiya is a essentially a boarding house where geisha live. It is run by a proprietress who is almost always a former geisha who helps train recruits (shikomi-san) into maiko (apprentice geisha). It is not a place where they work, only where they live. There are some okiya in which the proprietress also owns and runs a teahouse or bar, but that is considered a separate space and guests are not allowed in the okiya.
That dog, who's name is Chiro, actually belongs to an okiya, the Nishimura okiya in Gion Koubu. He's the most famous okiya pet, usually because he can be seen in lying in front of the okiya pretty regularly, like here: [link]