"Impending danger" and "imminent danger" are very similar and I'd say almost interchangeable, but 'impending' carries the idea of a looming threat that could happen at any time, whereas 'imminent' means the danger is happening very very soon—there's more of a sense of urgency in the timing.
Given that these puppy-related dangers are lurking nearby but could happen next week, next month, next year, etc., I would choose 'impending' 😊