Do you think that it's ok to sleep with your dog?

I just started dating a girl who sleeps with her dog (pug). I think that dogs don't belong in a bed/bedroom for a lot of reasons, in fact, I think it's down-right disgusting. I'm a true dog lover, but I also believe that dogs aren't people and shouldn't be treated as such.

After our first night together she voluntarily started putting the dog in its crate in the living room at night, because I think anyone would realize that you can't have sex with a dog jumping all over you. But of course, as soon as morning comes the dog is freaking out, jumping all over the bed, rolling on the pillows and spitting/sneezing all over the place the way pugs do. And I'm sure when I'm not around the dog is sleeping in bed with her as usual.

But it gets worse, the other night we were having sex and I could see dog hair stuck to her sweaty back! Ugh, what a turn off. It's getting so I don't really want to spend the night at her house anymore. (If she stays at my place she has to get someone to check in on the dog)

Do you think that it's ok to sleep with a dog?
What is the best way to let her know how disgusting I think this is?
How should I handle the situation?