I never heard that about QEII; if she said it, she must have paraphrased or "Bidened" (plagaraized) it.
Queen Victoria not only made a youthful pronouncement that "I will be good" (should she become Queen), but also supposedly did actually say “Oh, how I wish that the Lord might come during my lifetime." When asked why, she answered "I should like to lay my crown at His feet.”
ThankQ for that detail!