I am trying to do the same thing.

While we file our taxes by calendar year/quarter/month, most restaurants do not do their internal reporting by calendar month or year.  We report by 4/5 week periods. for example: 

For 2019, January's time period will be 12/31/18-1/27/19 (Monday-Sunday).  In 2018, January's time period was 1/1/18-1/28/18.  (Monday-Sunday)  Different dates!

I use QuickBooks Premier 2018 and this version does not allow for me to compare year over year or month over month using the time periods I need it to.  I realize that I can run a report using any dates I want.  But, when I want to do comparisons, budgeting etc, I cannot generate a report using the time periods explained above.  

Is there a version of QuickBooks that will allow for this?