They're really taking their time getting to wherever it is they're going.
"He knew no haste" is an old-fashioned way of saying Death didn't speed or hurry.
The shift from "We" to "He" in the same line is an important one. The "We" might allow the reader to think the speaker has some control over the pace, but Dickinson quickly reminds us that "He" is the one determining the relaxed progress and that the speaker's just along for the ride.
While we've already determined that the speaker is not afraid of Death, this slow pace still creates a feeling of drawn-out suspense in the poem and keeps us wondering what might happen.
And I put away My labor and my leisure too, For his Civility –
Lines 6-7 mean that she has given up work and free time (we might assume she's given up thinking about or worrying about them too).
Line 8 works a couple of ways. First, we can read "For" as "because of." So, she gave up thinking about work and play because Death is just so polite and charming that he distracted her from anything else.
Or, we can read the "for" as "in place of." So, similar to the first interpretation, she has given up the worries (work) and joys (leisure) of life in exchange for his graciousness. We might even guess that she is starting to feel more civil and social too.
Either way, the speaker seems pretty content with, if not a little gaga for Death.
If this were a first date, Death would be doing a pretty good job. She seems both happy and even a little impressed by his manners.