Couple of methods:
Create a number of expressions in chart, 1 for each column you want. The exoression would include the logic to include only the date applicable to that column. Use an iF or Set Analysis
Create a field in script. We call it something like Dim_Date_QtrAnd6Weeks. Two fields. One to display as x axis, other links to the date in your fact table. Create it with Qtr1 and every date in quarter1. Repeat for each column. Can have same date in two columns, qlikview won't mind. In chart use that as dimension, make sure to sort on load order though.