I wouldn't bother personally. This is the BA service standard. Experienced similar on 4 (out of 8) F sectors in the past 6 months.

Every single 787-10 I've stepped foot on in the past few months has had issues with suites in both F and J. These are meant to be the newest aircraft.

The seat I had on a recent SYD-SIN was filthy which is beggars belief given the aircraft sits at SYD for 8 hours.

Obviously the dog hair issue is nothing to do with them - you'd have to complain to AA, but I would suggest that is a waste of your time.