There are different solution, but why don't we start with the most easy one.
Why now use the Copy Master Detail wizard tool found in App Management and make a button to copy the parent and it's children. So instead of creating a new Parent Record (monthly report record) and then coxing last month's children to be copied into it (which is possible but a bit more complicated), why not just make a button to copy the parent with its children?
So the user would do that and then edit the record to update the dates or whatever needs to be updated for the New monthly report record.
