The Mrs. Darwin of the title, and the speaker of the poem, is Emma Darwin, wife of the famed naturalist Charles Darwin.
The poem itself then opens rather unusually: "7 April 1852." Sometimes poets include a date underneath a poem's title (before the first line) or at the very end of the poem (after the last line). That date usually indicates the day the poem was finished, and sometimes poets include the place of composition too. But in this case, "7 April 1852" is the actual first line of "Mrs Darwin," indicating that the poem is taking the form of a diary entry.
The second line is then short and bluntly descriptive: "Went to the Zoo." The brevity here adds to the sense that Mrs. Darwin quickly jotted these lines down in her journal at the end of the day.
Notably, line 2 lacks a subject: the speaker implies that Charles and I or We went to the zoo, but doesn't actually say so (that confirmation will come in the next line). The implied subject contributes to the poem's off-hand, informal tone, which is appropriate for a diary entry.
These first two lines are short and strongly end-stopped with periods, and they don't follow any particular meter. These qualities, like the second line's implied subject, add to the poem's informal feel. The lines do, however, share a subtle end rhyme between the "two" in "1852" and "Zoo." (There's also an internal rhyme in line 2: "Went to the zoo.") The rhyme is subtle; readers might almost miss it on the page given that it relies on a numeral. Still, it's a good reminder that, despite the poem's appearance as a diary entry, "Mrs Darwin" is still a poem—it would be odd for an actual diary entry to rhyme!
The tension between the poem's imaginative artfulness, on the one hand, and its historical plausibility, on the other, helps create much of the irony and humor that make "Mrs Darwin" so clever and memorable.