Austrian and German food tends to be very simple, yet still requires great skill.
When you eliminate pork, you eliminate the famous "Wiener Schnitzel" and "Jäger Schnitzel," among other things. Another famous food is their near infinite variety of dumplings. Sacher Torte is arguably their most famous desert, but wait to you go into an Austrian "Konditorei" (Bake shop), you'll explode at the selection.
Unfortunately, Germanic cooking isn't simple merely because it tends to use simple ingredients. There are many techniques displayed in their sauces and baking that can only come from experience and apprenticeships.
This is a cop out, as it is NOT a famous Austrian dish, just an everyday Austrian dish that is very simple: bring consomme or other flavored stock to a strong boil, take it off the heat, pour into a bowl, and then gently slip an egg yolk without any white into the hot broth and let it simmer gently a minute or two so that the yolk keeps its shape. Garnish with fresh parsley, if you wish. Serve. You will be amazed at what a pick-me-up this can be on a cold day, or what an elegant soup course it can make.