Welcome to the boards!
Pet-Friendly Housing List for Milaukee
As far as homes go, you may have to ask individual landlords about that. If they say that your dog is allowed, get it in writing. That way it doesn't come back to bite you in the behind later.
I hope this helps!
I just re-read your post. You're looking for apartments in Fredericton, not Milaukee.
I've been looking - but listings on the net are few and far between. Your best bet is to contact individual rental companies and ask them directly.