"Doggone" does a good deal of work in its title before the first line begins. As an exclamation, "doggone" is a mild, old-fashioned way of swearing, what you say when you're exasperated but would never curse. Split in two, it becomes "dog gone": a dog that has bolted. Bonta's poem plays on both meanings, and the result is a small comedy of escape in which it's hard to say who is escaping from what.
The first couplet borrows the shape of a solemn farewell. "I must take leave of myself" echoes the idiom "take leave of your senses," with the self swapped in for the senses. The word "must" makes it sound like a compulsion rather than a choice, and the speaker treats his own identity as something to be politely excused from, like a room or a conversation. The destination, "the land," is plain and deliberately vague. It isn't a wood or a meadow, just open ground, with no particular scenery to admire.
Then the poem swerves. "dog like a poem / I could not contain" arrives with no verb and no introduction, as though the dog had simply bounded into the sentence. The simile can be read in two directions. The dog may be a stand-in for the poem, or the poem may be as unruly as a dog. "Contain" is the key word here. It means to restrain, as with a leash, and also to hold as content, as a poem holds meaning. A quiet paradox follows from this. If the speaker has already left himself behind, who is left to do the containing? The poem hints, and this is an inference from the wording, that the self is the container and the poem is whatever slips out of it.
The last couplet is where the sound takes over. "laughing in the midst / of a most serious mist" leaves the laugher unnamed. It could be the dog, the poem, or the speaker, newly unselved. That grammatical looseness is useful, because by the end the three have blurred together. The line break after "midst" lets the word hang for a beat before "mist" arrives, and the two words differ by a single letter, as if the mist were a "midst" with something dropped. The hissing s-sounds of "most serious mist" suggest a hush, the sound of someone being shushed. The mist can be read as real weather over the land, and also as the heavy gloom of high seriousness, the damp solemnity poetry is sometimes expected to wear. Calling a mist "serious" is a joke in itself, since mist can't be anything of the kind, and the laughter in its midst punctures the pose.
The construction is as light as the content. The poem is three couplets of short lines, running from seven syllables down to four ("dog like a poem") and back up to six. The tightest line is the one where the dog bursts in, and the final line stretches slightly as the mist spreads. There is no end rhyme, and there is no punctuation at all. The first couplet is a complete sentence, but the second and third are fragments, so the grammar loosens at the same pace as the self. Even the capital letters are telling. The only ones in the poem are the two uses of "I," so the self being abandoned is also the only thing the page marks as important.
The poem is significant because it turns a familiar idea upside down in about thirty words. Poetry is often pictured as self-expression, the "I" speaking its mind. Here the poem comes only when the "I" steps aside, and what it brings is play rather than wisdom. The poem doesn't explain this. It lets the dog run, and it trusts the reader to follow, a little out of breath and probably smiling. That seems to be the point: a poem you could fully contain wouldn't be worth walking out into the mist for.