I think it's doable in 6 weeks. Depends on how you like to travel and how many hours you want to drive each day.
To give you some type of reference, we took a trip from WNY to Yellowstone and the Canadian Rockies - Jasper and back home in 5 weeks. That included multiple day stays at Mount Rushmore, Yellowstone, Grand Tetons, Glacier, Banff, Jasper, and we only drove about 4-5 hours a day.
Mary & Tom (aka Hutch)
2015 Jayco Eagle Premier 361REQS
2014 GMC Sierra 3500HD 4x4 CC D/A
Sunlines: 2005 Solaris T-280SR; 1999 Solaris T-2670; 1998 Saturn T-24A