Khazad Dum

[Legolas]

What Return of the King had to say about dwarves post-War of the Ring:

After the fall of Sauron, Gimli brought south a part of the Dwarf-folk of Erebor, and he became Lord of the Glittering Caves. He and his people did great works in Gondor and Rohan. For Minas Tirith they forged gates of mithril and steel to replace those broken by the Witch-king.

In the line of kings Gimli wrote out for Aragorn, Durin VII is noted to be the last.

It does seem likely that the dwarves attempt to reinhabit Moria (yet again), but it's possible that those that left the Lonely Mountain or the Iron Hills were so captivated by the Glittering Caves and their works for Rohan/Gondor that these new, precious resources made Moria seem like old news.