Realistically, what you need is dogs, plural. There's a reason almost every culture in the world has a history with them.

And a pack of them, breeding as you go, is going to be the best way to keep surviving because they can be trained to be guards, alarms, hunters, fighters, hot water bottles, and they can be food in a real emergency. That last one sucks to think about, but sacrificing one or two so that you and the pack can keep alive is just what you have to do.

Don't get hung up by thinking a given breed is ideal, because it won't be generalist enough. You just get medium size and large-ish dogs, and train the succeeding generations as best fits their abilities rather than trying to breed for specific jobs.

Dogs are also imminently personable. You'll be alone, or not able to trust other humans. Having animals that can fulfill our social needs is vital, and dogs are our best option for that long term, in a survival situation.

Now, if the apocalypse is a bit less dangerous daily, keeping a population of chickens, and goats is a good idea. They'll serve as alarms easily, and can be food or food producers. They're both easy to tame as well, if you start young.