I live in Ottawa and there are a lot of people who do live in apartments with dogs. Most do tend to be smaller dogs, but I've run across pet owners who are renting and have large-breed dogs as well.
Rent here does tend to be rather high, but sometimes you can get lucky and find a place that's reasonable (sometimes rentals in private homes can be good). You could always try looking into OCH (Ottawa Community Housing) as they do have a geared-to-income rent; I don't know much more about it than that though...i.e., if there is a very long waiting list, for instance, but they do allow dogs, as long as the owners are responsible in having the pet not disturb others, clean up after them, etc. Here's a link to their website:
Renting from OCH
And here's a link to a list of regulations and rules when renting in Ottawa:
Ottawa Rental Rules - Ottawa Apartment Rental Guide
A bit of a heads-up about Ottawa and dogs...this city has very strict regulations concerning dogs. If you have a vehicle it makes life a lot easier, but if you don't, be aware that dogs - and any other pet, even as small as a mouse - are not permitted on any mode of public transit (bus, go-train) and while there are a lot of parks in the city, most either have very strict leash laws (dog not allowed off leash) or they are not allowed in the park at all. Conroy Pit is one area where you can take your dog and they can run off leash, it's set in a large semi-wooded area and can get very crowded on the weekends. But again, you need a vehicle to get there. There are a couple of pet taxi services operating her, but that's all. Something to consider if you don't have a car.
Afraid I can't offer much more than that, but best of luck to you!