If you have space at home you could get a play yard? I have the Haenim play yard at home with 6 panels which measures 2m x 1m if put it up in a rectangle. Then I put the play mat inside the play yard. Then at least the dog won't shed the fur directly on to the play mat?
My parents as well as my in-laws have dogs. During the CNY I told them to fence up the dog. The dog was very unhappy but no choice because my boy is very sensitive to fur and dust. He's slightly asthmatic.