Your stepper motor looks to be the same make/size as the one I use. Mine runs 2" per revolution (rack and pinion) and handles about a 10# load OK. Since you have what appears to be .2 inches per revolution (5 pitch leadscrew?) you should have no problem with it. Also, since your Z carriage has weight AND you will no doubt add a router head (or ??), do you really need anti-backlash nuts for it? When will the down force exceed the total weight?
If you can give me the max ecpected Total Weight, I can calculate what the stepper can handle and reply to you.