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When you're done with iCal, just close the window, but don't quit the application. This will leave it running in the background, but it shouldn't have any noticeable impact on system performance.
This topic surfaces regularly, so I think Apple are aware of its annoyance. You can further encourage them by sending feedback to http://www.apple.com/feedback/ical.html
The icon could be manipulated by a number of applications, like the iCal background processes or the Finder, but there are probably reasons why it isn't done yet.
Applications can change their dock icon only while they are running. Apple should consider using an icon that doesn't show a date while iCal isn't running.
You can have the menu bar clock show the day of the week and click on it to see the current date.