Not exactly. Most Austrians were clamoring for war, and Germany simply gave their support for their own reasons. That's not the same as Germany pushing an unwilling Austria into war. Serbia was viewed by Austria in much the same way that the USA viewed Afghanistan in the 1990s and 2000s - a failed state that was actively promoting terrorism and needed to be tamed.
Saying that WWI was started by militaristic Prussians is a legacy of the heaps of propaganda that were shoveled out by the Entente during and after the war. All the nations involved were very militaristic. That was simply the nature of European society at the time. If Prussia did not unify Germany, there may not have been the specific circumstances that historically led to WWI, but general war in Europe would probably have happened anyway. For example, if Napoleon III was not kicked out in 1871, he might have incited a war against this hypothetical mega-Austria, with similar results. Similarly, the collapse of Ottoman authority in the Balkans created a powder keg that surely would have drawn in the Great Powers in some form - especially in this scenario where a more powerful Austria is competing with Russia in the east.
In short, the carnage of the early 20th century was not caused by Prussian militarism, though it certainly contributed to it like everyone else. It was caused by geopolitical factors combined with the culture and military theory of the time. It's even more ridiculous to say that Prussia was responsible for the Nazis. The Nazi Party was already a mass movement and the SA had over three million members before the Prussian military establishment was brought under Nazi control.