I doubt this is a coincidence.
No, but it sure is bullshit.
So, to wrap this thread up before abandoning it completely, The Queen has no need to attend cabinet meetings, nor has any monarch since, as mentioned, bloody ages ago. She attended as part of her 60th year on the throne, and who knows, we might be repeating this story on her 70th year too.
As for Antarctica, the landmass owned by the UK is to be named in her honour. Hardly the same as the Queen deciding to wrap up warm and fly south for the winter, is it?