I have cats, the filter is supposed to filter the allergens out of the air, but the hair stays where it is. The appliance doesn't suck anything in, I guess only a hoover can help against the hair.

The appliance cleans the air very efficiently. But just that: the air. And since I have to assume that most of the cat hair is on the floor, the appliance might not really be suitable in your case. But I'm not speaking from experience, because I don't have any animals at home.