Ontario law is that no landlord can evict you or deny you rent because you own a pet (no matter what the pet or breed). Find a place that you like, check out the lease agreement with regards to pets (though that will never hold up anyways, not sure why landlords put it in there), don't tell the landlord about the pet and move in. Just make sure that your dog is not an excessive barker and doesn't do any damage to the property and you should be fine. If the landlord says anything to you, remind him or her that you are aware of the Ontario Landlord Tenants Act and cannot be evicted due to owning a pet. This is what I found off one of the links but you may want to Google the actual Act.
Ontario Landlord and Tenant Act; questions and answers PETS AND "NO PETS CLAUSES":
Q6: The landlord says I must either move out or get rid of my pet; Do I?
A6: Only if the pet is dangerous, causes allergic reactions or causes problems for other tenants or the landlord, must you get rid of your pet or consider moving elsewhere as per Landlord application to terminate tenancy based on animals.
Even if you signed a lease with a "no pets" clause, if the pet is not a problem for anybody they can not enforce it; such no pets clauses are invalid under the law.
You do not have to move or get rid of the pet unless the Board issues a written order to do so.