I bought our dog about 14 months ago over from DEN to LHR on BA. I used a pet transit company out of Denver, cost about $2,700 all up (more than my club world seat on the same flight!), they handled all the custom's clearance stuff at LHR and delivered to the door. I imagine there are similar companies in the SF area.
Edit: There was specific stuff we had to do with vets within 7 days of travel, we booked the trip about 3 months out.