How can we measure the air quality index of our room?
Depending on you local codes and the type of work being done, the construction contractor might be required to monitor her project's environmental impact.
As already stated, testing equipment can be expensive to purchase for private use, but Code Enforcement or the contractor might be able to help you out with a loaner of some type, or even perform an IAC test for you.
Great question.  Please let us know how it turns out.