@Rkk92 the goal of letting IRCC know is to avoid getting invited to a test / oath you cannot attend (well, mainly before covid for the test, now it's a 3 weeks window...)
The chances of being invited to a test in December in your case are pretty slim anyway given the current timelines, and you have no obligation to notify them, but there's no reason not to do it, once you get your AOR (and only after you get your AOR).
As for the stamps, doesn't matter.
Also, FYI, I was in a similar situation, got my AOR a couple months before a vacation, sent a web form, and received a test invitation while in vacation, for a test date a couple weeks after I'm back. Sending that webform worked well enough in my case...