The Tories just repealed the Fixed Term Parliaments Act meaning the PM has sole power to call an election.
It is a constitutional convention that Boris should resign if he loses the Vote of No Confidence, like Thatcher did, staying in post until a new leader is chosen. But that is a mere convention and not legally binding, plus he has shown he doesn't care about ignoring those.
There is nothing in the Dissolution and Calling of Parliament Act 2022 which empowers the Queen to say no to a request. In fact, the 2022 Act explicitly states that the courts cannot involve themselves in adjudicating a question of dissolution. If Johnson wants to call an election, there is nothing to stop him from doing so. I don't recall a monarch every refusing a request to dissolve Parliament.