Now that the ruling has been given can't the queen herself ask for Boris' resignation?

It's my understanding that the queen has the right to choose and possibly fire her prime minister at any time she likes. And in fact she could choose anybody but she tends to choose the leader of the party with the majority in an election.

Surely as Boris has put her in an embarrassing position she could do this? Although admittedly it's unlikely and could be viewed as undemocratic surely lying to the queen. Further to that Boris and the Conservatives no longer hold a majority in parliament.

I imagine the queen won't do anything but she's well within her rights to do so.