You could do a re-direct, but that is probably not what you are looking for because it will result in currentdomain.com being displayed in the URL bar.
You also haven't told us if the app you are working with is wordpress, but nonetheless, the situation will be similar.
First thing you want to so is make sure desiredomain.com is fully hosted USING THE SAME USER as currentdomain.
Next, go into wp-admin and update the url to desiredomain.com, you will get an error, ignore it for now.
Next, open your FTP program and
Rename currentdomain.com to TEMP
Rename desiredomain.com to currentdomain.com
Rename TEMP to desiredomain.com
This reverses the two domains, assuming you have made your change in wp-admin.
Once you have determined that everything is working you will probably want to delete currentdomain.com (which now most likely holds the dreamhost quickstart file from adding hosting under that domain) then once it is deleted, redirect THAT domain to desiredomain.com so that existing users can still find your site.