I will, but from my yesterday, her Airport was on but my Airport [physically connected to iMac by Ethernet] was off.
In any case, the printer is connected only to the iMac.

A test would be with my iMac Shutdown, i.e. off.

Later:
iMac shut down. iMac's Airport connection still not On. MacBook set to print an NWP page.
"Printer off line" is MacBook message after looking for Printer. 

iMac given Startup. Even before fully launching all files Printer began to, and finished, printing.
However, the Main Menu bar was not coloured white and only a few of the items therein were displayed. I needed to Restart to get Main Menu bar information and its colour back.

I have tried to add another printer to the MacBook but this did not seem to work. What it did do however was to install the printer as a Scanner. This would be due, I guess, to the MacBook having 'VueScan' installed. That's a great application still.

To be continued?
------------------------
Regards from brianF
===============

On 13/04/2011, at 7:40 AM, Jon Johanning wrote:

> On 4/11/11 10:30 PM, Brian Ferguson wrote:
>> However, it appears that her iBook uses its Airport link to my iMac and then to the printer. I assume that if I turn off the iMac she cannot print.
>> 
> I wouldn't swear to this, since I am no networking expert, but I think that if the iBook, iMac, and printer are all on one network, it wouldn't matter if the iMac were off -- but the Airport has to be on, of course. Try an experiment and see.
> 
> Regards,
> 
> Jon Johanning