My husband has been on PD for about 2 years. We were told that no, we should not keep the dog. We kept her. She is a Shetland Sheepdog who has long hair but does not shed much.
My husband is extraordinarily clean while setting up and connecting, washing his hands with anti-bacterial soap immediately before he performs any connection. He always makes sure to keep any open connections (bag to cassette, catheter tip to cassette, catheter tip to cap) horizontal or pointing down while connecting. He never allows an open connection to point up where gravity can send any contaminants (including dog fur or dander) into the open connection.
The dog has always slept with us on the floor in our bedroom.