Minutes ago, I was able to successfully beat 'Journey Down the Anduin'. Now I am setting up the 'Escape from Dol Guldur' adventure.

My initial draw from the encounter deck to attach to the 3 objective cards was as follows:

1 enemy, 1 treachery and 1 location

The enemy and location make sense as how I would claim the objectives, but I am not clear on how to resolve the treachery? Do I just draw again until I get a non-treachery card?

Nope. You resolve the treachery card and then you've got an unguarded objective.

So the treachery resolves during the Setup?

Do enemy cards resolve their When Revealed effects during the setup as well? Including Surge?

Yes to everything. You might want to check out the FAQ (the link is in my signature), as it contains the answers to many of these questions. For example:

(1.01) Encounter Keywords
Surge, Doomed, and Guarded keywords should be
resolved any time the card on which they occur enters
play, including during setup.

Since the guarded keyword "reveals" a card, the When Revealed effect will trigger during setup.

Thanks Radiskull

I've been through the rulebook a few times and was just making sure I was interpreting everything correctly.