The first. It just asks if you've ever tried tasting it, for fun or curiosity maybe. To ask if you've ever had to resort to dog food you might say something like "Har du nogensinde været nødt til at spise hundemad?"
Prøvede du at spise hundmad? = Did you try eating dog food? (Past tense, or datid in Danish).
Har du prøvet at spise hundemad? = Have you tried eating dog food? (Present perfect tense, or perfektum/førnutid in Danish).