Here is a good site for writing poetry explication papers. http://writingcenter.unc.edu/handouts/poetry-explications/. My suggestion is that you follow the steps on this site carefully while writing your paper. First, talk about the overall thing being dramatized, which in this case is death. The speaker is the narrator, so talk about the tone she uses to convey her meaning (somber, calm). The other characters in the poem would be Death and Immortality. The basic plot design is the journey from life to death. It tells you they pass the setting sun, so you can assume the action begins in the afternoon and ends in the evening. (Appropriate for someone who is leaving their life behind). The physical location is the carriage. Perhaps Emily Dickinson’s motivation is to explain the mystery of death, a mystery none of us can solve on our own.
Next, look at the form of the poem. Emily Dickinson does use a particular lyric form which really differed from anyone else. I think if you take a look at this site, it will help you with the form, syntax, and rhetoric she uses in general. http://www.emilydickinsonmuseum.org/poetry_characteristics Look at the poem and think about the words she uses to provide impact, such as kindly used in conjunction with death.
For the last part of your paper, look at rhetorical patterns, such as statements that take the same format, rhyme, patterns of sound, rhyme and meter. The site I mentioned in the second paragraph should be particularly helpful to you.