I would like to see examples of countries (areas?) which had no formal government and which hosted a sophisticated, peaceful civilisation for some length of time. I think I've read quite a lot of history and I'm struggling to recall any such place.
Medieval Iceland and Ireland didn't have an actual government, law was decentralized. I wouldn't call any medieval society "sophisticated and peaceful", but they compared well to other European places of the time.
There's also lex mercatoria which was a set of voluntary merchant laws that transcended states of the time.
There have been practical examples of decentralization of mostly everything a state monopolizes today, if not all.
I've actually read some Rothbard. I found his prose to be deeply unconvincing. I respect economists who develop theories and then test them against real world data. Theories that exist in the world of abstract philosophy is how you end up with the deflationary spiral idea - stuff that simply doesn't match observed reality.
Rothbard had a lot of very strange ideas about the nature of cartels and monopolies. DPR was fond of citing him as some kind of authority. But when you read his writings, where are the examples, where are the studies that show his theory matches observed reality better than other theories do? He didn't bother. He asserted some ideas as facts and then engaged in ever more tenuous logical extrapolations. My mind was open and what I found simply didn't win me over.
Empiricism may be used to demonstrate to skeptics an already proven praxeological theory, but it's not through empiricism that economic science should be done. The deflationary spiral theory is supported by empiricist economists, by the way - no wonder is so wrong. For empiricist scientific methods to work, you must be able to isolate all variables and reproduce experiments at will. That's obviously impossible when studying the human action. You can't even enumerate all possible variables, let alone isolate them. Economics can only be developed through the "apriori" method, the same method of mathematics: you start with basic axioms, and then you deduct logical conclusions.
Ludwig von Mises wrote a lot on the importance of the praxeological method to the economic science. Perhaps you should search his texts.
And by the way, libertarianism isn't only economics. Actually, I'd say it's more an "ethical philosophy" than anything.