Actually, that is a beautiful purse ! Since it is made with hair that the dog is shedding anyway, or that comes out when they are being groomed, it is not something that would harm the dog in any way at all.
I remember going through a museum once and seeing small items that were crocheted out of human hair, and this would not be a whole lot different than that.
From the looks of the purse, it looks like she actually spins the fur into worsted yarn before she then knits the purse.
This would be a lengthy process from start to finish. She would have to first clean the fur, then spin it into a soft yarn, dye it if it were going to be a colored purse, and then knit and decorate it.
I think that I would not want to spend that much money on any purse, no matter what it was made of, but it looks to me like she is not being unreasonable to charge that much money.