We did NY to UK on the QM2 a couple of years ago...it was absolutely fabulous! We travelled on the last eastbound crossing of the season (end October/beginning November) and it cost us under $800 each for quad occupancy cabin. I thought it was a fantastic deal considering that the price included lodging and meals for the 6 days as well as transport. Because we travelled from Utah I had to factor in the cost of travel to NY, but found a way cheap one-way flight. No trouble at all getting a train in Southampton to where we needed to go. We used a travel agent that specialized in cruises, didn't book through Cunard's website...
Also, QM2 does (did?) have kennel facilities on board, check the PETS scheme to make sure they're still an approved carrier.