queue_object.queue will return copy of your queue in a deque object which you can then use the slices of. It is of course, not syncronized with the original queue, but will allow you to peek at the queue at the time of the copy.
There's a good rationalization for why you wouldn't want to do this explained in detail in this thread comp.lang.python - Queue peek?. But if you're just trying to understand how Queue works, this is one simple way.
import Queue
q = Queue.Queue()
q.push(1)
q.put('foo')
q.put('bar')
d = q.queue
print(d)
deque(['foo', 'bar'])
print(d[0])
'foo'
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