Watson is a dog owned by the Foster (Freeman) Family. When Sophie chose to have her family's memories wiped, she requested that Alden give them a large yard so that they could get a dog. They ended up getting a beagle that her family named "Watson."
Watson, along with Marty, went to Atlantis with Sophie and Amy in Book 6: Nightfall. Apparently, he and Marty were quite vicious, shredding Alden's tunic sleeves to bits because they did not know him.
It can be noted that Watson is the name of Sherlock Holmes' companion in the Sherlock Holmes series, which is referenced throughout the KOTLC series.