I was upgraded to F four months ago while flying with a pet (as an MVP at the upgrade window).

However, I was assigned a bulkhead seat (where pets aren't allowed) and the system removed the dog from my reservation. I found out when I called AS to inquire about the bulkhead seat. They had to add the dog back onto my reservation and move me to a different row. So double check your booking if you are assigned to a window seat.