I have read before that the Queen retains the legal power to dissolve Parliament and to appoint the Prime Minister, even if that power has not been used for a very long time, and that such a procedure would be extremely irregular at this time.
You are right to a point.
The Queen only has the power to dissolve Parliament at 1) it's request or 2) if it decides to extend it's period of office. The latter i believe happened in Australia in the 70's. The Australian government decided to bring in legislation to extend it's time in power and the Queen stepped in. I cannot remember the details but i'm sure the info is out there.
She only appoints the Prime Minister at the request of Parliament. It is not her decision.
Paul