Hi,
Welcome to the forum and QU.
You set the dpi that is required wherever the dot is, see screen shot attached - I set the 300 and it does not change wherever I put the dot.
It's nonsense   In fact the Windows properties show 96ppi for both versions here.
The pixel size should be 4950 x 3510.
4590/16.5" = 300ppi
Remember, the so-called "DPI" (PPI to be precise) of an image is often some notional value and an image on its own does not have a real ppi until it's printed. It has a pixel size, that is all.
Check the pixel size and divide by the inches, that's the real ppi. If the pixel size is correct, it's ok.  
Terry

By the way, did you make a PRINT by clicking Print as if you were printing to paper?
That's what you will give to your printer or whoever.

Hi,
Terminology can be muddled sometimes!
PPI usually refers to the resolution at the time of printing: the inch size divided by the pixel size.
DPI, dots per inch is sometimes used to mean the same thing but when referring to a particular printer refers to the spry pattern of the nozzles and is is usually much higher than the print ppi.
That is what is required, despite the print supplier using "dpi".
I would not rely on that but check by dividing pixels by inches.
If you have 2 different pixels sizes for print optimised and web optimised then you must have used 2 different PPI settings in the print to File dialogue.
But what is the pixel size, same or different? If the same then a different jpeg quality was used.
I have double checked this here and wherever the dot is placed in the dialogue, I get identical images, same pixel size and just a modest difference in file size due to one having print sharpening which makes a larger file (+ 14%).
The differences between images for Online Printing and Monitor/Web are:
Online: print sharpening
Web: no print sharpening
Online: specify any printer icc profile to embed
Web: sRGB profile only
QU is behaving perfectly here. I suppose it is possible that the demo version has a problem but Print to File is a long established feature and no-one else has reported problems.
Terry

Thanks for explaining everything. After a lot of reading on the web I too am of the same opinion as you. Windows does not display the true DPI, and DPI is meaningless anyway.
In fact the PPI of the photo determines the print size. I took a lot of persuading but I am there now!

Today I trialed two other well known resizing applications and QImage Ultimate was the easiest to use by far. I am truly glad I took the time out to do that.
QImage is a time saver for me, even with the trial limitations of only four prints per job. It didn't take long to master either, I just had to trust it to do what it was designed to do!

Thanks again Terry-M. Sorry for disbelieving you at first, but I had to prove it to myself to come to the inevitable conclusion. QImage is probably the best print solution for the phographer out there.