Hi- My wife, dog and I just relocated to Zurich area too. (also from Ohio). We are curently living in Oberrieden,(20min by train to Zurich). I think homegate.ch and this forum are good resources for finding an apartment. You can always put a post in the apartment wanted area and give the details of what you are looking for and when you need it.
So, far we like Oberrieden, it has everything we need and several dog friendly parks along the lake within walking distance.
Where are you from in Ohio? We are from Bungal country

. Good luck finding a place.