The vanilla WoW Horde leveling guide you see on this site was originally made back in 2006 by Joana (AKA Mancow, or FuriousPaul). The guides have been tweaked many times over the years to make things "faster". The leveling guides were made because of all the messages I got from people asking me how I was able to level up so quickly on new realms. I was first to level 60 on 7 different realms (3 with Mancow and 4 with Joana), even winning Blizzard's "First to Level 50" contest they held back in 2006.
There are two parts of the quest chain for each continent. The first part involves defeating numerous Master Pet Tamers, and the second requires you to triumph over the Grand Master Tamer. After you've bested the Grand Master Tamer, dailies from each Tamer will unlock for that continent. All the dailies continue to reward experience for your companions, however only the Grand Master daily quest will reward the Sack of Pet Supplies.
If your pet's health gets too low or its attacks aren't very effective against a certain combatant, you can always switch out your current pet with another companion on your team. Only pets that are considered active (i.e., those in your three Battle Pet Slots), may be switched in and out during the battle. Once the match is over, you can always change up your active pet team, which is useful if one of your pets is low on health or dead.