Hi!
With the rel=canonical in place, this is a stronge hint to the search enignes that docbeans.com is the one that should be indexed. Is it possible for you to do a 301 redirect from docbeans.com/index to docbeans.com (or the other way around), then that would probably be even better(?). Are there any particular reasons for you to keep both, then this has to be taken into the equation.
Have you had the change to look at this page: https://moz.com/blog/301-redirect-or-relcanonical-which-one-should-you-use. It could be of some value for you to decide whether to just keep the canonical or to do a 301.
Hope this helps! 
Anders