The up-rezzing is done in Photoshop. Go to Image>Image size. Set the size of the print you want, say 11 x 14 and then with the resample box checked, set the resolution at 720. This creates an image that is going to print at 720dpi at the size you are printing.
If you are doing output sharpening, do it after you up-rez.
I normally print out of Photoshop and the setting there for Photo RPM is in the printer settings, third box under the Paper and Quality Options. I don't know how this will work with QTR. I would guess that you would want to set the Resolution to 2880dpi.