Austria was at XIX century a powerfull state, the fought against Napoleon at the first of XIX and with GB, Russia and Prussia they won. That powerful state have several territories at Balcans and they have a fight against Turkish later at mid century. So while Germany was trying to do the unification Austria had their own stuff.

On the other hand you can think why they didn't lead the unification of Germany. Cause it was done around Prussia, and of course Austria didn't wanna join under Prussia tutelage, and Prussia wasn't leave Austria de leading.

Hope you understand it. Sorry for my English and regards!

After the Napoleonic wars, the Holy Roman Empire was more or less disbanded. When the French were finally defeated, the German states were again drawn to a central authority in part due to tradition and in part due to the fact that German Nationalism (along with Italian nationalism) was in full force. Initially Austria, as head of the newly formed German Confederation, acted as this central authority as it did in the past; however, Prussia at the end of the 18th century was an established military powerhouse and was vying for power. The importance of German nationalism can't be understated in this. Austria's dominance bred a bit of resentment among the other German states and with Prussia's growing dominance in trade, many looked to them as rightful German leader, wanting to exclude Austria and it's far-flung empire.

Now, when some petty argument occurred over Schelsvig(spelling?)-Holstein (northern German province), the German Diet was convened and ended up with the famous Otto von Bismarck declaring the Confederation null, and the Austro-Prussian War essentially began. Without going into a ton of detail, Prussia's economic edge allowed them and their allies (Italy, a few of the German states) to win the war and resulted in the defeat of Austria. Several of the German states that fought with Austria were annexed or later joined the North German Confederation (created and led by Prussia with the intent to later create a constitution there from the get-go), several of the neutral states joined the NGC, and all of Prussia's allies (barring Italy obviously) joined the NGC. A few years later a constitution was drawn up and created much of what is modern-day Germany.

Although the only major territorial loss for Austria was Venezia (given to the growing Italy), they lost much more as their dominance of not only Germany was lost, but their dominance of their large empire also began to wane. Prussia and it's German nationalism movement always saw a unified Germany without Austria, so when Prussia won the war, it was not at all interested in the incorporation of Austria.

Source: Danilovic, Vesna. "When the Stakes Are High—Deterrence and Conflict among Major Powers" (2002) Balfour, M. (1964). The Kaiser and his Times. (It's an old source, but accurate)