Shifting a new site from temporary to permanent place

A site I host was being redesigned by someone else as the client never contacted me to see if I could do it 🙁

At any rate, it’s now showing up at http://www.royalexchange.com.au/rex and they want it shifted to http://www.royalexchange.com.au to replace the old site which was in html.

Is there anything I should know about shifting a wordpress site from a folder to the root folder? Or should I simply just do a redirect so that the domain directs to the folder address?