BA Exec Club has a minimum BA metal four-segment requirement for status-aquiring purposes, which, in your case, is going to be a problem (BA and guide dogs don't really mix well, which is part BA policies, part UK animal import regulations).
I`d go with IB unless getting your dog on BA flights hasn't been a problem for you.
Or stay with AA and employ some workarounds to get around the revenue requirements such as booking partner codeshares (if those exist on your routes!) where EQD/EQM/RDM earning remains distance-based. This works especially well for longhaul flights in premium cabins. A few good leads are in the 'AA EQD runs' thread:
2017 AA EQD Run