Praise be to Allah the Lord of the Worlds.
It is permissible to keep a puppy at home to train it to hunt or guard, in addition to other lawful purposes. Those purposes were excluded in the narration in which Sufyan bin Abi Zuhair Ash-Shani said that he heard Allah's Messenger (PBUH) saying: "If somebody keeps a dog that is neither used for farm work nor for guarding the livestock, he will lose one Qirat (of the reward) of his good deeds every day." {Related by Bukhari & Muslim}.
Al-Shirbini (May Allah have mercy on him) said: "It is permissible to keep a dog for hunting or guarding livestock and crops or protection while moving from place to place. It is also permissible to keep a puppy to serve the same purposes." {Moghni Al-Mohtaj, vol. 2/pp.342}.
However, it isn`t permissible to keep it without shelter as it could die from cold weather. In addition, making such mistake means abusing that animal and treating it mercilessly, which isn`t approved by the teachings of Sharia. Rather, it should be kept in a separate place outdoors to avoid infecting your children and removing its impurities, which require washing seven times; one of which with earth.
It is worth pointing that scholars have disagreed largely about the ruling on selling dogs that are permissible to be kept for a purpose. The majority have prohibited selling and buying those dogs. They said: "One who owns such dog is required to give it for free to whomever is in need for it. However, Hanafie scholars permitted buying it and stated that the prohibition pertains to the dogs, which aren`t permissible to be kept." And Allah the Almighty Knows Best.
