She is two months old? I would start introducing her to baths now. I would say once every other week or maybe once a week. Depends on how much time is spent outside/how muddy it is. Maci is almost 3 and she get bathed every weekend.
As far as first haircut... depends on if you want her to grow a long coat, or keep her hair short and more managable. If her hair is thick and cottony you may want to consider the "zhoie and joey" hair cut once she has some longer hair... it's super cute! you can search for it on here
