I say to do whatever you want. You own the building. If people question it just tell them that you are responsible for your dog and you don't want to be responsible for other people's pets. If I were to move into your rental I certainly wouldn't question what you do. You own the property.
I've been very wishy-washy about my pet policies. I used to allow them, but then had a crazy cat lady whose apartment smelled like a litter box. Then I had a lady with a really nice dog whose boyfriend moved in. He passed all of the checks and had a "really well trained" German Sheppard. Well, they locked each of the dogs in bedrooms during the day and that German Sheppard tore the door to shreds, along with the carpet under it. It also peed and pooped all over the apartment. Apparently it was really upset about the move. They were there 3 months and then moved out (month-to-month lease). Their deposit and pet deposit covered the damage, but I had to put in a new bedroom door and carpet, along with lots of other carpet cleaning. After that I outlawed dogs and cats.
Now I'm starting to think I should reconsider and accept small dogs under 20 lbs. I think they might come with residents that will stay longer. I will charge a $25 pet rent and $300 pet deposit, as well as be very clear that all rules must be followed. When I had bought the building 2 years ago it was winter time and the entire back yard was dog crap from someone's emotional support animal. He told me he'd clean it up in the spring when the snow melted. I think not!