If I am understanding you correctly, all you should need to do is go into the View UI and click on the clone link of the existing calendar view and then enter the new path in the page display and appropriate date field to use.
based upon your comment below, you could set a variable in a preprocess hook to the output of this view, eg:
and then you would have $cal inside your template to use however you wanted. If you needed this information inside of a node, eg in a text field that would be displayed between those paragraphs of other text, you could probably hook into nodeapi() and set it there on display of the node. If you need it embeddable inside a field amongst other text, that gets trickier, but doable with a custom filter of your own (or http://drupal.org/project/customfilter might be able to do it with their php filter but I've not used it personally) but then you'd have something along the lines of [calendar] that your users could have inside of a text field that would be transformed into the calendar view output on view.
Regardless of any of the above, I have no idea what CSS style issues you would have to fiddle with, if any, or what to do with the previous and next links of the calendar and if they would also work or not as expected on this new page.