I don't think you can do that with a report since it doesn't look like Reports have a filter on "date opened".
You should, however, be able to craft a query to pull that info. You could give your query a name and save it, then run it whenever you'd like.
Something like this:
In this case i went to Tickets -> Search Tickets -> Advanced Search and chose these fields (as an example):
Date Opened prior to 1 Month ago
Status is Open
and this is what i was meaning about if you save the query with a name, you can later choose it and run it ad hoc from a 'regular' view like My Tickets or Group Tickets:
...then you would just clear that query field to go back to the normal view.