The young witness of horror
Because Zlata is young-ish (she turns eleven during the novel), she is an ironic witness to the horrors of war, because her parents are experiencing war as the latest thing in an already very-difficult adult life, where perhaps they have made a pleasant life for Zlata, but not without enduring much, much hardship along the way. That's what makes Zlata's point-of-view ironic; this war is the most extreme bad thing that could have happened, and it happened to someone with almost no reference for what 'bad times' even were.
The deaths of animals
The family had pets that they loved, but they die. That's an ominous thing for the family to suffer. Any time an animal dies, it is a reminder of any person's own death, because after all humans are just animals, so when the humans have to watch their pets die in this novel, the war makes the experience way more extreme that they could imagine. Ironically, the simple death of something small, like a canary, is absolutely horrifying and unimaginable in the context of surviving the Serbian invasion.
The irony of education
When throughout the book, Zlata continues her education, she has to ponder the irony. What is the benefit of math and reading at a time like this? The benefit is that after a while, after she works through the season of literal isolation in the cellar, she gets to go to school with some other kids again, and when she gets there, her hope in the future is rewarded. So by looking past the horrors of war and focusing on the future, and she is able to focus on developing herself. But oh boy, that's hard to do when an army is attacking your community just upstairs.
The irony of politicians
Guess what the politicians do during the war—basically nothing. These pillars of power are suddenly vanished. They don't really solve problems very well. Why? Is it because all politicians are evil or something? Probably not—the novel suggests that actually, the irony of the government is that, because politicians are motivated by their own interests, they aren't usually willing to make the kinds of political sacrifices that it would take to get things back on track.
The ending
Even though American and European communities are fully aware of the war, they often neglect to help, and when the ending of the novel comes, the reader might wish that the war had ended (like Zlata herself wishes, no doubt). Something about the novel format makes the story seem to end wrongly, as if peace should be restored before the story ends, but that's exactly the point of the novel—for Zlata, the hell of war is long-suffered. They long for an end to come to their brutal suffering, but the war continues on seemingly forever.
