Calm down, your code has not O(n^2) complextity. You have a nested loop, but only one counts to N (the number of objects), the other counts to a fixed number of properties, which is not related to N. So you have O(N).
For the static variables, you write "there aren't any instance-specific properties", later you write about updates of the individual properties of your objects, which are exactly instance-specific properties. Maybe you are confusing the "class Properties" (which is of course shared among all properties) with the individual properties? So I think you don't need static members at all.
Do you want to display changes to the objects only if they appear, or do you want a continuos display? If your hardware is able to handle the latter, I would recommend going that way. In that case, you have to iterate over all objects anyway and update them along the way.
Edit: The difference is that in the former (update on change) the drawing is initiated by the operation of changing the values, for example a object movement. For the latter, a continuos display, you would add a QTimer, which fires say 60 times a second and calls a SLOT(render()) which does the actual rendering of all objects. Depending on the rate of changes this may actually be faster. And it is probably easier to implement. Another possibilty is let Qt handle the whole drawing, using a Graphics View, which handles the objects-to-draw internally in a very efficient tree structure. Take a look at http://doc.trolltech.com/4.5/graphicsview.html
If you want to display only the changes, you could use individual callbacks for each properties value. Each time the value of a property is changed (in this case making the properties vlaues private and using setSomeThing(value)), you call the update function with an emit(update()). If you are absolutly concernd about emit being slow, you could use "real" callbacks via function pointers, but I don't recommend that, Qt's connect/signal/slot is so much easier to use. And the overhead is in most cases really neglible.