Escort quests can take awhile to do. I have thoroughly tested all the escort quests in the game for time/xp. Most are worth doing, but as long as you are able to actually do them without failing. Most require you to pay special attention to the escortee as most are fragile and will die easily, so do your best to keep mobs off of the escortee during escort quests. The longest one in the game is the Tanaris chicken escort. The chicken escorts are only worth doing if you were able to do all 3 of them, as if you do, you will be able to turn in an additional easy quick XP turn in quest at BB, which makes them worth it.
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.