Ok so this is my very first guide in the site and in general so I hope you will find it helpfull!
First of all the deck Quest Druid, is a deck built around the new Saviors of Uldum Quest card: Untapped Potential. 
It requires you to end 4 turns with unspent mana,Ossirian Tear is excellent for a long-term value plan, 
as well as offering swift board swings through the combination of Choose One cards' effects.
This deck as the name suggests is a token-based variation in order to use the early game potential druid has to 
swarm the field with tokens and buff them once you quest is completed.

Mulligan Guide :

Generally you want to keep Acornbearer and Worthy Expedition everytime.Both are 1 mana cost cards which means a turn 2 play
and Acornbearer gifts you with 2 1/1 minions which can be placed later on to the field to create some pressure to the enemy.
Other cards you wanna keep are Dreamway Guardians(they are good both in early and in late game due to their lifesteal),BEEEES!!!,
Druid of the Scythe and Garden Gnome.The other cards are good as well but you don't really need them that early.

Druid/Rogue/Hunter Match-up :
In case you're facing a druid this is what you need to keep in mind : The person that will have true control over the board will win,
do not rush to complete your quest by using coin should you be second since he won't be able to do much in the first turn he activates
his power if you have answered most of his early threats(should you have the hand to do so)
Cards to keep : Acornbearer , Worthy Expendition , Druid Of the Scythe

Priest Match-up :
The priest match up is kinda tricky especially is he is using the quest(haven't met a lot of them so far so will probably update it),
what you wanna do in this case is to try to keep in your hand some good threats for when you complete your quest to beat him asap
since he is heavily dependant on healing his minions and hero to activate his quest
Cards to keep : Dryid Of the Scythe,Swipe,Oasis Surger,Tending Tauren 

Warlock Match-up :
Most of the warlocks atm focus around the quest which means you got until turn 6-8 to gain a heavy control over the board,
try to poke his face with every chance you get since he can't do much until completes the quest.But do not swarm the board while 
leaving your hand empty since an early hellfire can destroy your board and set your hand a few turns back.
Cards to keep : Acornbearer,Worthy Expendition,Dreamway Guardians,Oasis Surger

Shaman/Mage Match-up :
Probably the highest treats to the deck since both classes have Tier 1 decks.Both mage and Shaman have decks that focus on either
early mid threats or later game big minions.Your best course of action here is to keep your hand ready and answer any threats
that may appear in the board.
Cards to keep : Acornbearer,Dreamway Guardians,Power of the Wild,Hidden Oasis(trust me on this you need this since you will
probably use it at turn 6)

Paladin Match-up :
Paladin has many early game threats as he is focused on swarning the board and with his tip the scales combo he can be a really
nasty threat which can overtake you should you not be prepared.
Cards to keep : Starfall,Swipe,Dreamway Guardians,Acornbearer

Warrior Match-up :
While it can be easy to deal with should your hand be decent,he can stall the game and be a really nasty thing to deal with.
Again here you need to focus on simply answering the opponents threats till you complete the quest and swarm the board.
Cards to keep : Acornbearer,Worthy Expedition,Druid of the Scythe,Oasis Surger

That's all for now will try to update it soon with card replacements but till then stay safe and if you think I can improve
the guide please let me know!

Many thanks to Khristophesaurus Dinosaurus for the wonderful video he made showing my deck!