I have been dealing with Qimage and the cop out line, "It doesn't happen when I print with other programs", for over 10 years.
I have heard people tell us that the 8 x 10 prints chop off heads in Qimage but 8 x 10s from "other" programs do not; prints too large, too small, pieces missing as in your case, and no pieces missing when printed from the other guy.
It is either a missed item in Qimage like the crop scissors, or you have a white border turned on and that shrinks the image on the paper,   OR, all else, it's the driver.

There's a factor to bear in mind, Qimage remembers the driver settings, and Lightroom, PS et al do not. So any scaling or markers turned on in the driver while in Qimage, will stick.
If you print from another program, you start with Plain Paper, and all the default settings.
So if you have something in the driver turned on as a marker or something, it will stay on.

The next factor. The HP drivers have earned the reputation for being very buggy, The worst part is they never fix them.
Why does the bug show up when printing with Qimage and sometimes not with another software?
The answer is in the chunks of data that Qimage sends to the driver being larger and more detailed. Some drivers cannot handle the data size and speed and choke on it.

My point is.... Concentrate on trying to find out what is causing the problem by calling and writing HP.
Make your point to them that the lines only happen with my new HP printer. Never had the lines before.
Otherwise, you have given them wiggle room to ignore you.

Please read,

http://ddisoftware.com/tech/articles/february-2010-the-hp-b8850/

Good luck!
Fred

Thanks for the follow up.
Good for all of us to keep stuff like that in the back of our minds so we can help the enxt person that reports similar problems.
Fred