The National Center for Transgender Equality has a great overview of passports as they relate to gender identity, including the application process.

The current policy permitting the change of gender markers on passports was facilitated by the Obama administration’s Department of State, and we are likely to see changes to the policy after January 20, 2017.

Several organizations have begun to gather funds to help people cover the cost of expedited passport changes:

 

Note that an active passport is a necessity for relocating (temporarily or otherwise) to anywhere else in the world, including Canada, so it is a very good idea to have one current and matching your other forms of identification.  You can begin the application process here.  It is possible, though expensive, to get a passport in just a few weeks.  Those in the process of a gender designation change may be issued a two-year limited validity passport which can later be replaced with a full passport.