[Voronwe]

This matter is mentioned in Appendix A and the Tale of Years:

We have heard tell that Legolas took Gimli Glóin's son with him because of their great friendship, greater than any that has been between Elf and Dwarf. If this is true, then it is strange indeed: that a Dwarf should be willing to leave Middle-earth for any love, or that the Eldar should receive him, or that the Lords of the West should permit it. But it is said that Gimli went also out of desire to see again the beauty of Galadriel; and it may be that she, being mighty among the Eldar, obtained this grace for him. More cannot be said of this matter.

Then Legolas built a grey ship in Ithilien, and sailed down Anduin and so over Sea; and with him, it is said, went Gimli the Dwarf. And when that ship passed an end was come in the Middle-earth of the Fellowship of the Ring.

So Gimli's passing into the West is perhaps more than just speculation, but certainly not a definate fact.

-Voronwe