I was wondering if there was a way to open a new instance of Toplevel() and close the current one via the press of a button, i.e. close the current window and open a new one
Yes, it's possible. To close an instance of Toplevel simply destroy it. You'll need to save a reference to the window. In your case I would either have Q1 destroy the window, or make a separate function that calls Q1 and then destroys the window. It all depends on what the main purpose of Q1 is.
For example:
def start(self):
...
self.new_window = name_w
...
def quit_window(self):
self.Q1()
self.new_window.destroy()
If you have multiple of these you might need to store the window references in a list or dictionary, but the basic mechanism is the same: use .destroy() to destroy the window.
This isn't the only way, of course. You could use lambda or functools.partial and a function that accepts the name of the window to destroy, or you could use nested functions, etc.