The title suggests the clocks have just been shifted, and the poem catches the strange fog that follows. The speaker feels thrown off, as if the day has arrived at the wrong hour. "Old as my own hat" is a playful, slightly weary phrase: the morning seems stale and familiar, already used up, even though it has barely started. Then "the morning at noon" adds to the confusion. The body says one thing, the clock says another, and the two don't line up.
The second stanza turns inward. The speaker and the night are paired as if they were two tired companions, "drawing up our unrest." That could mean gathering it together, or pulling it up like a blanket or a chair. Either way, the night hasn't really left. The restlessness lingers into the day. The mood is groggy, quietly humorous, and a little lonely, the feeling of being out of step with time itself.