I made this quest druid for fun but was very surprised when I got winstreak :D. Against highlander priest I have 7-0 winrate so that already means something. Allover winrate is about 50%.
Firstly I have to say that the I am a F2P so obviously the deck is not in the best form it could have been. Personally, I would love to have for example Kun, The Forgotten King here.
The deck strategy is to basically finish the quest early with your beasts and then pull out the big creatures. It's also very nice to ramp quickly. Against aggro/tempo decks it's crucial to have your Spreading Plague in hand. Without this and Malfurion The Pestilent I would have lost almost every matchup like this. The combo core of the deck is Menagerie Warden which helps you a lot with finishing the quest and can create incredible value. My favourite combo is copying Charged Devilsaur :D. When you finish the quest you are likely to draw zero mana minions from your Nourish or Ultimate Infestation. Sadly, often you have to use Ultimate Infestation before Barnabus The Stomper. I don't run second one because of that it's very likely to mill yourself then. Fun fact is that yout opponent often doesn't know how to play against this deck archetype XD.