Gypsum by itself is one of the best products one can use in these cases as it basically is completely inert material.
- The problems can start popping up when they use recycled paper, add special chemicals (mold resistance), or it absorbs vocs from somewhere / something else.
- With proper care and storage regular drywall should be the least of your worries.
The same goes for standard mud (gypsum based) which is what many companies also use for the texture. With that you can always ask to see the MSDS sheets for all products used and see if any of the items are known problem makers for you.
As for the primer, paint, and caulking - I would also recommend you view those products' MSDS sheets for what chemicals are used.
There have also been quite a few questions asked and answered by others here at GreenHomeGuide.com on specific items and brands before with some including the ever important - does it hold up?
The best advice I can give is cover your bed in plastic and ventilate the area well before you go back in. In many cases if they say a product cures or stops off gassing in 1 day I will ventilate the area for 3 days.
For more information:
Also, read Nick Cope's Q&A "Is there a drywall alternative that's safe for our new baby's nursery?"