The poem sets two very different moods side by side. In the first couplet we get a bleak scene: hard rain and wind battering a "plague house," a place of sickness and fear. The weather feels as grim as the title's promise of a time of plague.
Then the speaker turns inward, and the tone shifts. They say they walk in "so merry a company" that they might "die with laughing." It's unclear who this company is. It could be real friends, imagined companions, or the people shut in together. Judging by the contrast, the speaker may be finding warmth and humour against the dread outside.
The last line is darkly funny, because dying and laughing are tied together in a place where death is a real danger. The mood is defiant and bittersweet. The poem doesn't deny the fear; it suggests that joy, even a slightly reckless kind, can be a way of surviving it.