WoW Classic seeks to recreate the "vanilla WoW" experience—that is, WoW as it existed before a series of seven game-altering major expansion packs from 2007's The Burning Crusade to 2018's Battle for Azeroth. To achieve this, Blizzard has rebuilt the game based on archived data from back in 2005 and 2006 (patch 1.12 is the goalpost—the current game is on patch 8.1.5). The company has committed to meticulously presenting the experience exactly as it was back then—warts and all—with only a small number of unavoidable or critical changes.
Each battle that you win will yield experience for each pet that participated. However, deceased companions will not receive any experience (so make an effort to keep them alive by swaping in a different pet). Experience gains are based on your pet's level compared to the wild pet. Defeating a higher level opponent will grant more experience than a much lower level one, but be ready for a tough fight!