This is difficult to answer because, in the current version of the game, we do have the option of placing animals in the Serenitea Pot. However, the same animals will not be able to accompany us during our travels across Teyvat. A few versions ago, Genshin Impact introduced Seelies that can accompany Travelers, similar to mini companions, and this could be the closest we would come to having a pet. However, do not be discouraged; there are many, many, many versions of Genshin Impact coming ahead, which would mean that we could potentially get pets that act as companions, or if not, players would have to settle for Paimon.