I'm suppose you could implement this in a subclass, but it would be
inefficient.  You'd have to over-ride put() and get(), call qsize(),
then delegate to Base.put() and Base.get().

A cleaner solution would be in the C implementation of deque, in
Modules/collectionsmodule.c.  There's just a couple of places where
queue->len gets incremented.  All that needs to happen is add:

if (queue->len > queue->high_water_mark) {
    queue->high_water_mark = queue->len;
}

after each one and then add the appropriate accessor functions in deque
and Queue to expose it to users.  The run-time cost is a couple of
machine instructions for each item added to the deque.

If I were to write the code and submit it, would you be willing to
accept it?