Peppers, technically, are perennials, like tomatoes, but mainly grown as annuals. They can survive into a second season if kept warm enough with plenty of light but production drops away as the plant tires. You'd get a better crop from a fresh plant next season.
Just bear in mind that they take longer to germinate than toms and longer to grow to plant-out stage. You need to start seeds very early. Or, alternatively, buy a mature seedling.