Nostalrius Begins - Quality wow vanilla realm (1.12)

So basically I was just leveling my Gnome in Dun Morogh until I got to that quest where you sneak into the
Thunderbrew Distillery basement and give that Dwarf guy a mug of Thunder ale so that he can go away and allow you to replace the kegs. I did it, but because I read all of the quest text, the keg despawned before I could accept the quest (The keg despawns when the Dwarf guy comes back from upstairs to drink his ale). Did I really break something or is it a bug?

You can try dropping the quest & starting over. Also check the bugtracker to see if it's been reported already. Remember, only you can prevent bugs.

There is no quest; after turning it in to that barrel, it gives the next one, which I couldn't accept.

Try buying him another ale or wait for someone else on the quest to do it and snag the barrel that spawns when he goes up the stairs.

That's probably qhat I'll end up doing.

That's what you get for playing a gnome.