[Man-of-the-Wold]

In the final analysis, Gimli's fate is a mystery, but a great one.

The peace thing really applies only to Bilbo, Frodo & Sam, as they were Ringbearers and could not peacefully live out their days in Middle-Earth, although with Sam it was as much to see Frodo again; I also see them essentially taking the places of Elrond's children. Nevertheless, we are to believe that in time, which may not correspond to any particular Middle-Earth Year, they indeed died and left this world.

As for Gimli, his reason for wishing to go to Elvenhome, and remarkably, being admitted, was his love for both Legolas and Galadriel.

Just as Tuor was evidently given the privilege of staying forever there in some place and context with Idril, it would be more conceivable if Gimli was given some such special dispensation.

Actually, in my mind it is less likely, however, because Gimli was not as singular as Tuor, and I also believe Tuor and Idril do not dwell with everyone else in Eldamar/Valinor, and for Gimli there would not be much point unless he could live freely among his various friends.

But in a sense it is more conceivable (though I believe not) that Gimli might be allowed to live forever there, because Dwarves are not "mortal" in the same sense as Men, and by implication, "Hobbits."

In Middle-Earth, their bodies do show signs of age, and they do experience failings of eyesight and agility, but not it would seem the debilitations and illnesses visited on Men. Theirs is also a very long earthly existence, lasting centuries, before they die naturally.

At that time, there is only confused indications of what happens, but it does not seem that they depart the Circles of this World like true Mortals, whose spirits and bodies are of different natures.

Rather, my sense is that Dwarves go to spend the rest of eternity in the "timeless" Halls of Mandos ... "to the halls of waiting to sit beside my fathers, until the world is renewed. ..., and go where [gold and silver] is of little worth, ..." Thorin, The Hobbit.

Then, it may be believed that the Dwarves arise and aid Aule in the remaking.

This is what I believe happened to Gimli, after he had again seen Galadriel and (probably at least) Sam (and possibly Aule). He finished his days like any other of the Khazad (joining Dain, Balin and Gloin), except oddly enough his passing occurred on Tol Eressea, representing possibly the final reconciliation about Elves and Dwarves.