To add onto what Kishore gave you, creating a string will obviously muck up your sorting. (Feb comes before Jan alphabetically). To get around this, you can include the actual (continuous) Month-year set as a discrete dimension (make it a blue pill on your shelf) in front of the calculated field that makes the string value. Then, just right click the blue Month pill and uncheck "Show Header." Now the field will be present to sort, but won't be visible.
If you need further assistance, please post a packaged workbook.
Thank you for sharing your idea. It is another thing that I learnt new today.
I agree on Mark for sorting issue for a string formatted date column and here is my suggestion for handling the sort.
Since, I have a case where I should consider the hierarchy for month-date formatted to string, I usually sort as per the actual date field. This can be done using: right click on the <Formatted Month Column> or in your case the RequiredDate field and click on sort: here under Sort by, I select the Field option, then select the actual date column and for Aggregation: I select Minimum(for Ascending order for date). This way, I always have my string formatted date in the ascending order.
Hope this helps.