This is just a "short" summary of what lead to Austria being excluded from a united German state, as the whole story of what happened then would not be shorter then the Wikipedia page of the Austro-Prussian War ;)

You're right, Austrians were always "Germans" like Bavarians or Prussians were. But as you already said, they were all seperate kingdoms who just happened to all speak German and were loosely united in the Holy Roman Empire until 1806 when Napolean took them all over. After having defeated Napoleon all German states united under the German Confederation. This Confederation wasn't really "Germany" as a Country but just a loose Conferation between all the German Kings, helping them to undermine the democratic and nationalistic Revolutions in the States. As the nationalistic forces became stronger, the leaders of the states saw the urgency to create one German state with one king or emperor, to create a counterpart to the large French national state. The two most powerful German states were Prussia and Austria. Prussia prefered the "Kleindeutsche Lösung" which would exclude Austria, Luxemburg and Liechtenstein from the newly founded German state, because of the reason, that in the "Großdeutsche Lösung", which would have included Austria, the larger Austria would have had all the power, what obviously Prussia did not prefer. After a war between those two and their allies in 1866, which Austria lost, Bismark wanted to realize the "Kleindeutsche Lösung", but the southern German states like Bavaria or Baden did neither want an German state under Prussian leadership. So he first formed the "Norddeutschen Bund", a Confederation of the northern German states. Only when Bismark faked a thread from France in 1870, the southern states joined the state, which formed the "Deutsches Kaiserreich", the German Empire, which existed until the end of WW1.

Hitler, Austria-born, annexed Austria in 1938, stating that it was a German state and called whole Germany the "Großdeutsches Reich", referring to the Plans in the 19th century.

After WW2 Austria was again formed into an seperate Country.

Source: "Geschichte und Geschehen", Ernst Klett Verlag

I'm just going to quote my post I wrote on this topic in another thread with a similar question (even though /u/hansi27 already mentioned most of it).

This question was the centerpiece of a huge debate at the time of German unification - the debate between the "kleindeutsche Lösung" (~small Germany solution) and the "großdeutsche Lösung" (~large Germany solution). "Small Germany" being Germany unified with Austria left out, and "large Germany" being Germany with Austria included.

The root of the conflict stems from the upheaval brought by the Napoleonic wars that dissolved the Holy Roman Empire (of the German Nation), the former overarching political structure of the German region. The Austrian Habsburg dynasty had controlled the HRE for a long time and wasn't willing to let it go completely, so they pretty much retained the title of Emperor for the state of Austria-Hungary itself.

Now, at the Vienna conference after the final defeat of Napoleon, the victors decided on a new political structure for Germany: The "Deutsche Bund" (German Confederation). In the German Confederation, Prussia and Austria were the leading powers with Austria being the nominal head of the confederation.

This is where a lot of the controversy stems from: Neither of the powers was being ready to submit to the other, a conflict that would cumulate in the "German War" (as it is called in Germany, while it's called Austro-Prussian or Seven Weeks War in the rest of the world) of 1866. Now, Austria was not without allies in Germany proper: Most of the "middle states" (medium sized states sandwiched between Prussia and Austria, such as Saxony or Bavaria) were fearful of Prussian expansion and sided with Austria in hopes of support. The "big Germany" solution thus was the solution in which Austria would retain the lead in Germany and grant extensive federal rights.

The Prussians on the other hands favored a more centralized approach and weren't all that much for extensive federalism, founding the "Zollverein" (German Customs Union) in the early 1830s. This Union was primarily aimed at standardizing weights, scales and such and lifting customs at the borders of member states, making transportation of wares and trade in general much cheaper and easier. But it also cemented the Prussian hegemony over the member states, since the Prussians gained extensive rights and the member states had to give up important state rights, becoming client states in all but name.

Also not helpful was the problem of Austria not being only Austria, but Austria-Hungary. Austria-Hungary was by no means Austria with Hungary as a nice little vassal, but rather a personal union. The Hungarians had gained extensive rights in this union over the time and were not without say in it. Also, Hungarians were not German and were not included in the German unification movement or forming German nationalism. Proponents of German unification with Austria included always retained that Austria would have to dissolve the personal union and leave Hungary excluded from Germany. But Austria was not really ready to just give up the larger part of their territory, just to become leader of a Germany that they considered to already control via the German Confederation anyway.

So, Austria was not really invested into the whole German unification thing anyway. And while Prussia wasn't really either, the King of Prussia vehemently refusing to become German emperor (even though being offered the crown by representatives of the 1848 revolution), Bismarck saw in the growing unification movement a perfect vehicle of ensuring Prussian hegemony over all of Germany and of defeating the ancient rival Austria once and for all.

Thus Bismarck stood behind the "small German solution" and pushed for it, leading to the German war (/Austro-Prussian war) and the exclusion of Austria from the unified Germany.