Death is introduced right away. We're also reminded that our time of death is not something we choose (at least that's what the poem claims), but something that is determined by forces beyond our control. This is also the start of the "why worry about things I cannot change?" attitude of the rest of the poem. There is no resistance to death, and no fear of it.
We slowly drove – He knew no haste (5)
Again, we're reminded that death is in control. He's in the driver's seat (literally). Also that death isn't always a quick thing. We are really shown the dying process in this poem and that, for the speaker, it was not a "life flashed before my eyes" kind of thing, but more like "my life crawled away slowly." The pace reflects the peace the speaker feels with death.
We passed the Setting Sun – (12)
Once the sun goes down, and death is lingering around, there's probably not a lot of hope for life left. Think of the sun setting as the symbolic closing of the eyes of the deceased. The lights are out, it's cold, and it won't be warming up. This is her final sunset.
We paused before a House that seemed A Swelling of the Ground – (17-18)
Well, this is the speaker's final resting place. The journey is over and their last stop is the grave. The speaker continues with the cool, calm, and collected approach to her death, and even seems hopeful by describing the grave as a house. Maybe she will finally feel at home there.