Hi Jet. (Fabulously cool name.)
Until someone can suggest a fix for what is happening on your end, here is what is working for me using Moodle 2.3 and Firefox 18.0.1 or Internet Explorer 10.0:
From Settings → Grades → Categegories and Items → Simple View - I am selecting the Move icon for the grade item (one click - no dragging). Please notice that under Quizzes, my "New Quiz" item is last. This is the item I wish to move.
After clicking on the Move icon (up and down arrows for those who may not be able to see my image clearly), I get the dashed "Move Here" boxes with black arrows. Notice in the screen capture below, that my New Quiz item now has the word (Move) next to it.
By clicking on the dashed box of my choice, the grade item moves to that position - so that in the next screen capture, my "New Quiz" is now in the first position within the Quizzes category.
And of course, Save Changes.
I hope this proves useful.
Michele Edwards, New York