Your reading of the poem makes sense. It might help to know that the dark trees are symbolizing the future in this poem. The second line tells us that these trees rarely show a breeze. This means that we cannot predict the future.
In the fourth line, Frost expresses his wish that those dark trees in the first line were stretched away to the edge of doom. This means that he hoped that the future is stretched far away. So, the edge of doom means here far away (in time). This seems consistent with your view, since it is also used in that way in the sentence you quoted, "Our marriage will last unto the edge of doom".
Based on: Analysis of "Into My Own".