My dog would like to accompany me to the restaurant. Is this possible?

Yes, of course! Your four-legged friend is welcome to come as your +1, but please with a muzzle and lead and only on the floor – even if the chair is tempting.
Special provisions on the Allgemeine Leinen- oder Maulkorbpflicht (Stadt Wien)  (General muzzle or lead obligation (City of Vienna)).