Regarding  the advice re color conversion, I have dug deeper into the ACDSee system that I am using.  (I did mention that I was largely ignorant of how the program works)!  I have used ACDSee for a couple of years, and found it a simple way to post process. However, my use of Qimage has now led me to a new understanding of what is happening in the background of ACDSee.  The program allows two methods of post processing DNG files, either 'Develop' or 'Edit'. I have been using the edit option.  After processing, this option does not allow changes to be saved as DNG, so I have saved them as Tif, which in turn allows them to be saved without a profile attached, or with an sRGB profile.  In my ignorant state, I saved them with the sRGB profile, and then converted them to RGB 1998 as a further step. Since my discussions on this forum, I have investigated the 'Develop' option, and found that it allows me to save my changes as DNG files with the RGB 1998 profile attached.  This is giving me a resulting file that prints well in ACDSee, and much better in Qimage. I no longer have the excessive magenta cast that caused my query in the first place, and now have a much greater understanding of what goes on behind the scenes. 
I am reluctant to use Qimage itself for my post production, as it lack some of the controls I find useful, such as Perspective Control, and  the Repair Tool options. Also, I find its ability to selectively adjust the various color channels by means of slider controls to be very intuitive.

My grateful thanks to you all for your assistance. I am equipped now, I believe, to print with much greater confidence, and greater expectations of success. 

Re Fred's reply:  I have checked the screenshots he posted, and they are identical to my settings.
Re Admin's reply:  I have followed the steps enumerated, and my settings were correct.  Tried another print, with no improvement in the result.  I found some Epson matte paper, so changed the paper type in the printer settings and made a test print,but with no better result, so I am ruling out the possibility that the Canon paper is a contributing factor.
The images I am printing are from a Leica CL in Raw format, giving me DNG files. I post process in ACDSee, and save the result as a Tif file. 
I then convert the color profile from sRGB IE61996-2.1 to Adobe RGB (1998).  (My assumption being that this will give me a wider color range at the printer).  In ACDSee, this conversion process has a drop-down box headed 'Rendering Intent".  It is set to 'Perceptual', but has other options, namely 'Relative Colormetric, Saturation, and Absolute Colormetric.
Does any of this throw light on the situation?  I feel that I am flailing about without knowing what I am doing, or why I am doing it.

Thank you for your response.  To take your points in order:

I am using Canon Photo Paper Plus Glossy, and have selected 'Photo Paper Glossy' in the printer settings.
The profile box is set to 'Let printer driver handle color'.
I have no profiles made.  The printer Color Management is set to ICM.  There is no Host ICM option available, as was suggested in your pop-up window when I looked into Printer properties.  I hope this helps you to understand where I'm at.   I should add that my understanding of creating profiles is precisely zero.

Good day all,
I have recently begun using Qimage ultimate, and am beset with a problem whereby all my prints exhibit a strong magenta cast.  If I revert to printing from ACDsee, the color rendition is almost perfect.   I am using an Epson XP-970 printer, though I cannot imagine that is relevant to my problem, as it produces the desired prints when used per ACDsee.  Can anyone please offer a solution ?