I was trying to accomplish the same thing, with no success.
Possible Workaround: Adding the date field to a dynamic search and selecting appropriate criteria.
Some of the search criteria (at least for dates) seems strange - either a bug or a feature, depending on your view:)
If you want to search for records between certain dates (date 1 -> date2), if seems that the logic is >= date1 and < date 2. So to include date2 records, you would need to add a day to the end date2 to include those records.
Perhaps someone else has a better experience with quicksearch (or a better workaround).