The speaker starts with a small, almost solemn announcement: they have to "take leave of myself" and go outdoors. It sounds like someone weighed down by their own thoughts, needing to step out of their head and into open country. Nothing more is said about why, which leaves the feeling a little mysterious.
Then a dog arrives, and the mood shifts. The speaker compares it to "a poem / I could not contain," as if the animal is something too lively and loose to be pinned down in words, much as a poem can overflow its own lines. The title's pun, "Doggone," also hints at a dog that has bounded off, and perhaps at the speaker's own self gone missing.
The last lines are the lightest. The dog is "laughing" in a "most serious mist." The seriousness of the weather, and maybe of the speaker's mood, is gently mocked by pure joy. The poem feels playful, fresh, and quietly freeing.