Can the software do this interpolation and if so, how do I go about it?
Yes, but ...
1 - Qimage is an 8 bit program (like most drivers) so it's a waste of time & resource making a 16 bit image to print.
2 - there's no need to make a new image by using QU to interpolate to a new pixel size; QU does that automatically to the native resolution of your printer. Just print the original 13280x4746 pixel image to the inch size you require, merely specify 113" x 40.384" as a custom size in QU. Don't worry about ppi of the image or print, QU sorts that out for you.
3 - when there's a message about storage space, it's a Windows problem not QU. XP was not very good a memory management. You can see how much is available by clicking QU Help, hold the shift key down and click Analyse Current Settings On XP I doubt (from memory) that you get more that about 750MB. I get 2000MB with W7-64 bit. With XP you can improve a little by using the 3GB switch. You'd have to Google about that.
To calculate MB required M pixel width x M pixel height x 3 (for RGB) Eg. 13.28x4.76x3 = 189.6MB
4 - Your original 13280x4746 image should print easily on QU with XP; the larger version is a problem. NB. the QU printing process is a little different that making a new image in QU in that data is sent to the printer in batches so as not to overload the system.
I hope that helps but summarising, print the original 13280x4746 pixel image at your specified inch size and let QU do its magic with interpolation in the printing process. Also, use Fusion interpolation, it's the best.
Terry
PS. I assume you meant 752MB not GB!