A month might not be possible. First, you submit an application online which will be processed for background checks by the Canadian and U.S. Government authorities. Once you have passed those background checks, you will receive a "conditional approval" message and will be invited to schedule an interview at one of the NEXUS Enrollment Centres. If you want to use the airport kiosks (not just vehicle/vessel), you must schedule your appointment at a location that is equipped with the iris scanning machines--the Canadian airports are the most convenient if you live in the USA and will fly up for the day. (Unless you live near Buffalo or Seattle, I suppose.)

I seem to recall that when I logged in to set up my appointment, I had to wait about 3 weeks for an available slot that would work with my schedule. Appointment times depend on the station, but usually are Mondays through Fridays during normal business hours. Then, I simply used miles for a same-day round-trip to YYZ.

The whole process took about 2.5 months from first application to walking away from the airport with my NEXUS card. So, I think trying to do it in a month would be difficult, especially if you have anything in your record that could delay the initial "conditional approval," such as any immigration/customs violations, arrests, convictions, criminal proceedings, frequent relocations, or extensive international travel.

Note, also, that NEXUS does not work at DFW itself. As far as air travel is concerned, NEXUS is a program that operates strictly at US CBP preclearance stations at Canadian airports. If you want to become a GlobalEntry member, it is free and practically automatic if you are an active NEXUS member. But, you do need to go back into the GOES system and officially apply for GlobalEntry after you have your NEXUS card in hand. You should get an approval notification soon after (NEXUS membership qualifies you for GlobalEntry because NEXUS has even more stringent criteria).