Hey everyone. I've been thinking about this for a little bit and I have a question to pose.
As I have just the 4E PHB, other than the DMG and MM1, what books do you think will be essential/desired to have in your library when Dark Sun released.
Depends on how your are going to define the meaning of "essential".
I believe WotC will develop 4e Dark Sun in such a way that some DM could run a Dark Sun campaign without requirement of anything beyond the PHB1, MM1, DMG1, and Dark Sun Campaign Guide. So stripped down, IMO, that's all that would be required.
That said, I strongly believe that to get the authentic Dark Sun feel — a setting deeply ingrained with psionics — then one must include the PHB3 as well.
Yeah PHB3 
I'd also suggest Adventuter's Value #1, because of some weapons (nets etc were added iirc? I know they are in the Dragon Magazine Annual) but mostly because of alchemy
alchemy makes perfect sense for Athas, IMHO!
While not essential, if you do not have a DDi subscription, picking up the Dragon Annual would be worthwhile for the gladiator and Art of the Kill articles.
It also depends on whether your going to be a player or a DM.
For a player: I would suggest that you have the PHB1 and Dark Sun PHB. The PHB3 will contain Psionic classes if you'd like to make a psionic character. The PHB2 contains Primal characters if that's the route you'd like to take. Neither the PHB2 nor 3 are required however (playing the base classes in the PHB1 should be fine). An insider subscription is completely optional.
For DMs: The DMG1, the Dark Sun Campaign Guide and Player's are required. Access to the above mentioned books, just to be aware of the class abilities. The DMG2 is recommended if you plan on making an exotic game on Athas - there are some useful tidbits. I would expect the MM3 is all you need for monsters (more should be included in the Dark Sun DMG). The MM1 and MM2 would probably be recommended for more - but truthfully, if you're creative, the DMG1 (and 2) provide enough details to make your own unique monsters or modify the MM3 monsters.
Since the 4e books are light on lore and heavy on crunch, the original DS accessories like Slave Tribes, Elves of Athas, Dune Trader and Veiled Alliance will be very useful. Unless they completely butcher the setting for 4e, all that old material should still apply and will just need an injection of 4e statblocks where required.
I would guess that suppliments that are heavy in fluff would be good, like Ivory Triangle.