How can I get the "new bed" smell out of my daughter's bedroom?
There's not really much you can do to stop the off gassing of VOC's from that piece of furniture, you just have to wait it out.  How long it will take depends on the compounds used and the manufacturing process.

Your concerns are definitely valid, there have been many harmful health effects associated with VOC's.

Most of the time, this process happens relatively fast, though a week isn't all that long.  Maybe a couple weeks to a month.

I agree with the commenter that suggested you call the manufacture or distributor.  They might have some information on how long this will take.

In the future, you might want to consider furniture that is certified low VOC.  GreenGuard is a UL certification common in North America.