[Daniel Telcontar]

I have re-read the part, and come to some conclusions. In the Danish translation the word doom is not used, but fate. Some of the above posts are probably right about the proper meaning of the word doom. And Galadriel says, that Aragorn has come through darkness and achieved/received what he wanted. That means either that he has his kingdom, or his wife, whom he could only marry as the king of both Arnor and Gondor.