I've ridden through this area a few times, and it can be a very cahllenging ride. Every time I've gone through the Navajo Nation, so that's the route I know.
The conditions on the road aren't bad. Traffic is generally light, and the roads are well suited for cycling. The challenges come from the very long distances between towns and services, the harsh weather (although your times shouldn't be terrible), and the beautiful but desolate terrain.
If you ride through the Navajo Nation, be careful of relying on maps for locations of towns and services. They often show towns every 10 miles or so, but in reality there are only the towns of Tuba City, Kayenta, and Shiprock. There are occasional service stations between them, but make sure you can be self sufficient for at least 100 miles -- including water.
It's a ride like no other, but be ready for it.