What would your plan of action be if you survived such a plague?

I think in a lot of ways staying close to home would be too hard. Everything around you would be a constant reminder of what you had lost. Staying in cities would be dangerous. Not only the rats and other pests gone mad, but with everyone dying so quickly Typhoid would be rife. Fresh water can often be hard to find in cities, depending where you are of course. Disease would be everywhere, I would try and get out as soon as possible.

I would head to a coast, and cultivate a farm. You can fish for food until the farm is up and running, if you pick the right area you can have fresh water that is headed towards the sea. If things get too weird or funky, you can jump on a boat and sail somewhere else. If you can't find an inlet for fresh water, you can use salt water, and boil it in a pressure cooker and distill drinking water. You would never run out of salt, which would be heavily relied on for preserving a lot of food.

I would try and round up as many chickens, cows, goats, sheep, horses and any other animal I could find. Not only for food supply, but essential eggs, dairy, muscle power and general companionship. It would still be lonely, but a trusty dog/cat/horse doesn't care if you talk to it constantly.

As for stuff, camping gear and clothes to keep you warm/dry wherever you are, outside of that I would try and live off the land as much as possible. I would try not to take too much non-essential stuff with me, hook one of those geeky trailers up to my bike, and just pedal until you find a spot you like.

I also like the idea of using preexisting resources. Try and find some sort of windmill and sow wheat around it. In time, you can make flour and then bread, bake it in a campfire oven you dig in the earth, or make unleavened bread and cook it on hot stones.

Day to day food production would take up a decent amount of time, but it would be worth it, and life would be much more satisfying. Imagine drinking a beer you brewed yourself, made from hand threshed wheat. Eating pasta made from flour you milled, with eggs you helped nurture, with a sauce you made from tomatoes you grew.

I also like the idea of living in or close to an orchard or vineyard. Wine, cider, as well as essential vitamins. Fighting off scurvy would become a serious concern, as would general health and well being.

There's Always A Siren, Singing In A Shipwreck

Where I live in Lancashire the nearest house is about quarter of a mile away and the nearest small village with a shop is about 3 mile away, but I think even this relative isolation would only protect you for so long.
Some of the more remote Outer Hebrides would be best bet. Constant fresh air from the westerlies coming in from the Atlantic,