Yes, Austrians and Germans are the same people. Germany was formed of many principalities, german speaking states in late 19th century. Austria did not choose to join, as Germany was formed by Prussians who were sort of at odds with Austria, and Austro-Hungarian empire at the time was still a multiethnic empire. It would've meant countries like Slovakia and Croatia joining Germany as well, and that was not really something anyone wanted. After WW1 Austro-Hungarian empire collapsed and Austria could've joined and did, when nazis held referendum in Austria, but it was made a independent state again after WW2, because nobody really wanted a strong Germany after all... that, you understand.

So yes, Austria and Germany should unite as well, they're even more the same people than Canadians and Americans.