How do you clean this type of carpet ?

I got a carpet a couple months ago and my boyfriends dog is wrecking it . I shouldn't of got white but I thought it looked neat. This is what the carpet used to look like And My side . It's cleaner then the other side my boyfriends side. Mind the vaccume because I'm vaccuming and brushing it . This is what it looks like now. How do you clean it ? It's full of dog hair , it's not white anymore . Boyfriend said I can't bleach it because it's harmful for his dog . Ugh . Any ideas ? I really want to use bleach and water it down , maybe it will get his dog not to chew on it ? But I also don't want to hurt the dog . I do have a steam cleaner but i have to try and get the hair out first and it's HARD ! Forty doller carpet down the drain :( Oh and I still have wax it it also . The heating it up with a blow-dryer smeared it . π€¬