Where are downloaded documents saved on an iPad Air?

Where did you specify to save it to ? Unless you did 'open in' to copy it to one of your apps (you have an app that supports that type of document ?) then it will only be in Safari's cache (assuming that you were using Safari) and not accessible anywhere - an iPad doesn't have a 'downloads folder' or a file system, iOS is a sandboxed environment, everything is stored within apps.

Does the app that you want to copy it to have a browser within it that allows you to download it directly within the app ?

There is no downloads folder. They are stored wherever you specified them to be stored, i.e in whichever App you used with the "Open In" options them after download.

Otherwise they are temporarily stored in Safari, or whichever browser you used to download the document until you close the browser or tab.