Hi Gois!
Here is a method to easy complete the Pet Battle Dailys (Only Dailys, not the "Tamers of Kalimdor" etc. Quests)
1. Accept the Daily
2. Pet Battle a Friend
3. Win the Pet Battle (Your Friend can use Level 1 Pets for faster Battle)
4. Quest Completed
I had the Quest "Defeat Elena Flutterfly" in my Questlog and battled a Friend just 4 fun and completed the Quest.
Tested it with the Master Tamer in Winterspring and it doesnt work.
Will test more Trainers tomorrow.
(Pandaria Spirit Tamers would be nice, but i completed the Dailys today, so i cant test it)