Yes, you can do this.
First navigate to Customers/Advanced Search/Order History Search, and search for "Customers who have placed at most 1 order".
Then navigate to Orders/Advanced Search/Order Search, and search for orders in the order date range you are interested in, and hit Search at the bottom of the page.
Then click the Export button at the top of the page, and on the next page, for order range, check both of the following:
Results of Current Order Search
Restrict to Results of Current Customer Search
The results are the customers who placed only 1 order, and that order was placed in the date range you specified.