UPDATE 12:32 PST: According to the FAQ page for the upcoming Minas Morgul expansion, the Stout Axe Dwarf race is available today to anyone who pre-orders. The new race, as well as many of the cosmetic items included in the separate editions will hit your account once you apply the product key. The full content of Minas Morgul is scheduled to launch on October 29th.
It seems the thralls of Mordor are breaking out of their cells today, as the latest patch notes for The Lord of the Rings Online hint that they could drop with the patch itself.
Update 24.3 makes reference to translation issues for the Stout Axes in the "Known Issues" section, but doesn't explicitly state the Stout Axe Dwarves are arriving with today's LotRO patch. The overall patch notes are actually pretty light, providing changes to the character panels, adding stats on Isengard gear to bring it "in line with modern values," and more. However, not actual mention of the Stout Axe Dwarves being added to the game is mentioned in the patch notes other than the known issue.
You can check out the full patch notes on the LotRO forums. The maintenance is still ongoing for The Lord of the Rings Online, so we'll have to update this post once we are able to log in and check for ourselves. In the meantime, you can check out the Stout Axe Dwarves starting experience, and how their origins make me hopeful for more stories told by the LotRO team that may or may not be expressly detailed in the books.