In a SHTF type situation, I'd try to maintain 6 hens and 2 cocks ,"an heir and a spare". 2 separate and extremely secure pens, perhaps even housed in the enclosed porch. In a disaster meat and eggs would be a huge help and six hens would provide 2 eggs a day for each of my family. The roosters may be a surprise choice. But if you lose all your roosters, once your hens die you are out of luck.
I'd give the dog mercy with a quick shot in his sleep. No way a pet dog is going to survive an apocalyptic situation without being a huge burden
The goats I'd eat because they'd just starve anyway
Cats can support themselves better than most humans, so I'd leave them to it and they'd likely outlive us all