Danb6177,
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Yes, that die set will work, assuming it is their carbide set.
This topic is a little confusing to the beginner because, if you look at cartridge drawings, you will see your 9mm case is slightly tapered. Carbide sizing dies, with the exception described below, use a sizing ring that is a single diameter, so it resizes your case straight as far down toward the head as the die goes, rather than maintaining the taper. You can get steel dies that maintain the taper, but you then have to lube your cases to keep them from getting stuck, so it makes loading large numbers of the small cases more of a chore. An advantage to a die that resizes straight is it can resize longer cases that have the same head and mouth diameter, as the 9×19, 9×21, and 9×23 do. It means you only need to own one sizing die for all of those cartridges.
The only drawback to sizing tapered cases to a uniform diameter is the brass gets worked a bit more and will wear out sooner back near the head. However, 9mm brass is so plentiful, that the economy of going to the extra expense required to get a carbide resizing that maintains a bit of the taper (Redding NexGen dies) is questionable. You could also get an old-style tapered resizing die in steel, but I don't recommend this if you intend to produce much volume, as it means having to lubricate the cases before resizing, whereas the carbide sizing ring dies do not.