I Need to Cask a Favor

Unfortunately, this quest sets you up for failure the first time. It leaves a multitude of details out of the quest text:

First and foremost, this is a timed quest. If you do not complete this quest in under three minutes you have to go back to Kharanos. The timer in this case is the time left on the buff from interacting with the quest object.

Second, the "brewery" in Kharanos is the Inn, the Thunderbrew Distillery.

Now you must run. Upon interacting with the cask outside the Inn, you are given a temporary buff. This buff has just enough time for you to run back to the quest giver. You cannot fly, you cannot cast, you cannot hearth. The running animation is forced. You have no choice but to hoof it.

Finally, on first read skim, the quest objectives can be confusing due to order. You must first acquire the cask in Kharanos and then deliver the cask to the quest giver.

Just found out an easy way to do this if you are a mage. I'm Alliance, so I dropped the portal to Ironforge a few feet in front of the barrel. And when I picked up the barrel, I clicked on the portal and was able to keep the barrel on my back and run to the cook to turn it in. Saves so much time. :)

There will be a beer barrel outside the inn at Kharanos. When the barrel is activated you will receive a backpack that will boost your run speed and a three minute timer will begin. Upon activating the barrel you will immediately be propelled forward(I was dismounted) so be sure to aim yourself toward Ironforge first. Deliver the ale back to the quest giver before the time expires. A Brewfest hat was also applied to my character's head for the duration of the timed segment.