Well, the speaker is a ghost, which means Dickinson had to believe in some sort of life after death (and we do know that she grew up in a Christian family). But she leaves specific religious references out of the poem, and we don't know if the speaker is recalling the memory of her death from Heaven, Hell, or somewhere else; we only know that it's a place beyond this world.
The formality of their slow progressions is supposed to mirror a traditional religious death procession.
The spirituality of the speaker belongs to no formally-established religion, but is her own personal belief system.